LIBRARY UNIVERSITY OF CALIFORNIA. Class dYSICAL LABORATORY EXPERIMENTS HEAT BY H. M. GOODWIN, PH.D. ASSOCIATE PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Printed for the use of students of the Massachusetts Institute of Technology, not published. SECOND EDITION. BOSTON : GEO. H. ELLIS Co., PRINTERS, 272 CONGRESS STREET. 1904, 3STOTE8 ON PHYSICAL LABORATORY EXPERIMENTS IN HEAT BY H. M. GOODWIN, PH.D. ASSOCIATE PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY. ' f UNIVSRBfT X^4 or :. .',:.._., L__ Printed for the use of students of the Massachusetts Institute of Technology r not published. SECOND EDITION. BOSTON : GEO. H. ELLIS Co., PRINTERS, 272 CONGRESS STREET. 1904. C COPYKIGHT, 1904. BY H. M. GOODWIN. s; , I TABLE OF CONTENTS. PACK PREFACE . 5 TIIERMOMETRY: General Discussion 7 Mercurial Thermometry Parti 14 Mercurial Thermometry Part II 22 Air Thermometry 27 Pressure and Boiling Point 37 CALORIMETRY: General Discussion . 42 Specific Heat 55 Latent Heat (51 Mechanical Equivalent 1 67 Mechanical Equivalent II. (Continuous Calorimeter) .... 72 EXPANSION 77 APPENDIX, Tables 78 1 30899 PREFACE The following notes cover the experiments in Heat which are required of students taking the General Laboratory Course in Physics. The laboratory work is performed subsequent to or in some cases concurrently with the lecture course on Heat. Little or no attention is, therefore, devoted in these notes to theory, deduction of formula^ etc., a knowledge of which is presupposed. On the other hand a detailed discus- sion is given of experimental methods, manipulation, sources of error and attainable precision, these matters being regarded of paramount importance in all work performed in the physical laboratory at the Institute. The cuts have been made from drawings of the actual apparatus used in the laboratory, and the description of the apparatus and procedure is given in such detail that the student is expected by studying his notes carefully before the exercise to be able to begin work at once" on entering the laboratory without further reference to them. As most of the experiments described require about two hours the usual laboratory pe- riod for their completion, preparation for the work prior to the exercise is essential. Many of the questions and problems at the end of each experiment require a knowledge of Precision of Measurements for their solution. These may be omitted by those students who have not had a course in that subject. H. M. GOODWIN. FEBRUARY, 1904. THERMOMETRY GENERAL DISCUSSION These notes should be carefully studied before performing the experiments on Mercurial or Air Thermometry. General Methods. Thermometry is the art and science of temperature measurement. Any property of a substance which varies in a well known manner with its temperature may be made the basis of a system of thermometric measurement, and we find extensively used at the present time methods based on the following changes produced in bodies when heated or cooled : a. Change of volume: gas, mercury, alcohol thermometers. b. Change of electrical resistance: platinum resistance ther- mometers. c. Change of thermo-electric force: thermo-electric pyrom- eters. d. Change of viscosity : effusion or transpiration pyrometers. In addition to these methods should also be mentioned specific heat pyrometers and optical pyrometers. The indica- tions of the latter are based on the intensity or quality of light emitted by bodies at high temperatures. The term pyrometry is usually employed when referring to methods applicable to temperatures above 300 C. The particular property or method which is best adapted to any given case depends of course upon the problem in hand as well as upon the actual temperature to be measured. Modern engineering as well as pure science demands methods covering a range of temperature from that of solid hydrogen 257.2 C. (Dewar, 1901), only 15 above the absolute zero, to that of the electric furnace, over 2000 C. Of the several instruments mentioned above, gas thermome- ters are applicable over the widest range of temperatures. 8 NOTES ON PHYSICAL LABORATORY EXPERIMENTS When filled with hydrogen, they may be used down to near its point of liquefaction (252.5 C., Dewar, 1901) and up to the highest temperature which a porcelain bulb will withstand, about 1400 C. A nitrogen thermometer can be used at even a higher temperature in a platinum-iridium bulb. Hydrogen diffuses through such bulbs at high temperatures. Gas ther- mometers afford the most accurate, absolute method of ther- mometry which we possess, but require considerable skill in their manipulation when a high degree of accuracy is desired. Several convenient commercial forms of less precision for high temperature measurements have, however, been perfected. Mercury thermometers are far more convenient for ordinary use, and are applicable at temperatures from 20 C. to 550 C. A high degree of perfection has now been attained in the con- struction of these instruments, due in a large measure to a careful scientific study of the nature of the glass best adapted to withstand high temperatures without change. Fused quartz has also been reJpently (1903) proposed as a suitable substance of which to construct thermometers. The utmost precision attainable with the best modern instruments is 0.003 from 0-100, 0.1 from 100-200, and 0.5 from 200-550. Below the proper range of mercury thermometers, which be- come unreliable considerably above the temperature at which mercury freezes, 39 C., thermometers of similar construc- tion but filled with alcohol, or better, toluene, are often used. Less convenient, as they require complicated electrical auxiliary apparatus, are the electrical resistance or platinum thermometers, applicable at all temperatures, from the very lowest up to about 800 C. With these instruments tempera- tures can be measured to 0.001 up to 100; 0.01 from 100- 500; and 0.1 from 500-800. Another instrument which of late years has rapidly and deservedly come into very general use, is the thermo-electric pyrometer, available at all temperatures up to the melting point of platinum, about 1700 C. This instrument is sensitive to 0.01 at 400 and to 1 at 1700 C. With a suitable galvan- ometer it may be very conveniently adapted to commercial work. THERMOMETRY 9 It is to be especially noted that, although both platinum resistance and thermo-electric pyrometers may have the high precision specified above when used in conjunction with suit- able galvanometers, the accuracy of their indications in absolute degrees depends fundamentally on the accuracy with which the temperature of the melting or boiling point of various sub- stances such as naphthalene, benzophenone, sulphur, gold, silver, etc., which are used for calibrating the pyrometers, is known. Such fixed points have been determined with the hydrogen thermometer. The pyrometers mentioned are there- fore essentially secondary instruments depending upon a cali- bration which ultimately goes back to the hydrogen standard. High temperatures may also be more or less accurately determined by several types of optical pyrometers, transpiration pyrometers, specific heat pyrometers, and others. The following notes include a discussion only of mercurial and air thermometry of ordinary precision. They apply to the calibration of mercury thermometers ranging up to 350 C., and correspond to a precision not greater than 0.05 C. between and 100, and less than this above 100. For a discussion of the various methods of pyrometry mentioned above the student is referred to the Laboratory Notes on Heat Measurements by Prof. C. L. Norton, or to Le Chatelier's and Boudouard's "Mesure des Temperatures elevees" (English translation by George K. Burgess). For the calibration and preparation of the highest grade thermometers the student should consult Guillaume's standard treatise on " Thermometrie de Precision," and the publications of the Reichsanstalt and of the 'Bureau des Poids et Mesures International. Units. The fundamental scale of temperature measurement is based on Thomson's (Lord Kelvin's) absolute thermodynamic scale, which is independent of the nature of any thermometric substance. The unit of temperature on this scale is called a degree, and has been chosen for convenience to coincide with a degree of the centigrade scale as defined below. The abso- lute scale is very nearly realized in practice by either a con- stant volume or constant pressure hydrogen thermometer, for the 10 NOTES ON PHYSICAL LABORATORY EXPERIMENTS deviations of this gas from the laws of a perfect (ideal) gas have been shown by Joule's and Thomson's porous plug experiment to be so small that they are probably not greater than the experimental errors inherent in the best thermometric work. The hydrogen thermometer without correction has been adopted by the International Bureau as the practical, ultimate standard of thermometric measurement, and represents at the present time the absolute scale of temperature as nearly as it is known. Measurements of temperature by other instruments than the hydrogen thermometer, not excepting even air or nitrogen thermometers, should therefore, if their accuracy warrants, be reduced to the hydrogen scale. The Celsius or centigrade scale of temperatures is that uni- versally employed in all scientific work. A centigrade degree is T(T the temperature interval between the temperature of melting ice under 760 mm. pressure and the boiling point of pure water at the same pressure, these two fixed points being denoted by and 100, respectively. The value of a degree on the absolute scale and on the centigrade scale is, as stated above, the same. The zero of the former is, however, 273 below that of the latter. The relation between the two scales is T = t + 273, where T and t are expressed in absolute and centi- grade degrees respectively, and 273 = o.o uWr, the reciprocal of the coefficient of expansion of hydrogen gas at constant pressure. The Fahrenheit scale, still employed (unfortunately) in much engineering work, is so graduated that the temperature of melting ice under standard conditions falls at 32, and the temperature of boiling water under standard conditions at 212. One Fahrenheit degree is, therefore, T i?r of this tem- perature interval, from which it follows that one degree Fahren- heit equals f of a degree centigrade. Any temperature on the Fahrenheit scale is reduced to cen- tigrade degrees by the expression tC = ^(t' F 32), or conversely THERMOMETRY 11 On the Continent the Reaumur scale is often employed in daily life but never for scientific work. On this scale the temperature of melting ice is taken as 0, and of boiling water under standard conditions as 80. Hence one degree Reaumur is equal to f degrees centigrade. Mercurial Thermometers. The best type of mercurial ther- mometer for general scientific work is one with a cylindrical bulb of about the diameter of the stem and with the graduations etched directly on the glass (a, figure 1). The graduations should be equidistant and should represent as nearly as may be, degrees or some simple fraction thereof. The capillary should terminate in a small bulb at the top to facilitate separat- ing a thread for calibration purposes, and also to prevent acci- dent in case of over-heating. When the total range of the thermometer is limited to a few de- grees, and it is desired to use it at widely different temperatures, as, for example, in boiling or freez- ing point determinations, the capillary is provided with a cistern at the top as shown in b, figure 1, by means of which the amount of mercury in the bulb can be adjusted and the thermometer made to read at any temperature. In certain casea when the thermometer is to be used only over a limited number of degrees at two different tem- peratures, as, for example, in calorimetric work in the neighborhood of and at room temperature, the unused interval, (5-15), is removed by blowing a small bulb of proper volume in the capillary just above the 5 division (c, figure 1). This device avoids making such sensitive calorim- eter thermometers of excessive length. In many thermometers of German make, the stem of the thermometer is a small capillary tube, back of which is placed a white porcelain, graduated scale and the whole inclosed in a protecting glass tube (d, figure 1). These thermometers are easy to read and are convenient for many purposes, but the scale is liable to move, the thermometers are Fi 12 NOTES ON PHYSICAL LABORATORY EXPERIMENTS bulky, and for anything except relative measurements are less desirable than those described above. Sources of Error. The temperature indicated by a mercurial thermometer is subject to the following sources of error, which must always be investigated and corrected for in thermornetry of even moderate precision, i.e., where an accuracy of 0.1 C. or more is desired. First. Errors arising from irregularities in the diameter of the bore. The correction for this source of error is known as the "calibration correction." Second. Errors arising from the fact that often a portion of the stem of the thermometer is exposed to a different tem- perature from that of the bulb. The thermometer will, there- fore, read too low or too high, according as the bulb is above or below the temperature of the stem. The correction for this error is known as the "stem exposure correction." Third. The error resulting from the so-called "lag" of the thermometer.. The correction is referred to as the "lag ice reading." This often serious source of error requires further explanation. It arises from the fact that glass, after under- going a sudden change of temperature, does not return imme- diately to its original volume when its initial temperature is re-established, but lags behind. Thus, if a thermometer has been heated to say 100, and is then suddenly cooled to 0, the volume of the bulb will remain temporarily too large and the ice reading will be too low. In the course of time the "zero" will gradually rise as the bulb contracts and returns to its original volume. The converse will of course be true if the bulb is strongly cooled and the temperature then raised. The amount of "lag" depends on the composition of the glass, on the duration of heating or cooling, on the temperature to which the thermometer is heated, and on the rapidity with which it is cooled from this temperature to zero degrees. On rapid cooling (e.g., in one or two minutes) from 100 to 0, ther- mometers often show a lag from 0.1 to 0.5, according to the kind of glass of which they are made. The time required for the lag of a thermometer to disappear, rapidly diminishes the THERMOMETRY 13 higher the temperature. Thus the lag resulting from a sudden cooling of 100 would be several months in disappearing at C.; a few days at 100 C., and only a few hours at 200 C. It is evident, . therefore, that the lag observed in any case de- pends to some extent on the previous history of the ther- mometer as well as upon the immediate change of temperature. As the bulb of a thermometer is necessarily very strongly heated during the process of construction and filling, the zero point of a new thermometer is often observed to rise con- tinually, sometimes by several degrees. This change in the volume of the bulb is known as "ageing" of the thermometer. It may often be removed and always reduced in amount by a process of annealing, i.e., heating the thermometer for several days or hours to a temperature above that at which it is to be used, and then allowing it to cool very slowly. Thermometers treated in this way are now prepared by some French makers; they are marked "recuit," and are usually much superior to others. The best thermometers are made at present either of "verre dur" in France, or of "Jena Glass" in Germany. Fourth. Errors due to the value of one scale unit not being exactly one degree. This arises from the fact that the ice and steam points are not exactly 100 scale units apart. Fifth. Errors resulting from the deviations of the ther- mometer from the absolute or hydrogen scale. The correction is known as the "reduction to the hydrogen scale." In high grade thermometry, i.e., where an accuracy greater than 0.05 is desired, corrections are also sometimes necessary for the external pressure on the bulb of the thermometer which may cause its zero to vary; the internal pressure of the mer- cury column which varies with the height of the column and the inclination of the thermometer; and for capillarity, which causes the indication of a thermometer to vary according as the mercury meniscus is ascending or descending. To eliminate the effect of internal pressure the International Bureau recom- mends that thermometers be read in a horizontal position. 14 NOTES ON PHYSICAL LABORATORY EXPERIMENTS MERCURIAL THERMOMETRY PART I CALIBRATION AND SCALE UNIT OF A THERMOMETER Object. The object of the experiment on Mercurial Ther- mometry is to give the student a practical working knowledge of the proper procedure in measuring temperature by means of a mercurial thermometer with an accuracy of 0.1 C. The experiment is divided into two distinct parts: Part I, the cali- bration of the thermometer and the determination of the value of its scale unit; and Part II, the use of a thermometer as illus- trated by the measurement of a definite temperature the boiling point of some liquid with particular reference to the correction of all sources of error affecting the result is 0.1 C. or more. Apparatus. A thermometer will be assigned to each stu- dent, to which he should attach a tag bearing his name. At the end of the exercise thermometers are to be returned to an instructor for safekeeping until the next exercise. After reports on the completed experiment (including both Part I. and Part II.) have been handed in and accepted, the thermometers with their receipts are to be returned to an instructor, who will credit them to the student if found in as perfect condi- tion as when delivered. The thermometers provided (a, figure 1) are graduated in centigrade degrees, and have a range from about 12 to + 112 C. The graduations are equidistant and etched directly on the stem. The end of the capil- lary terminates in a small bulb blown at the top of the ther- mometer. Parallax correctors in the form of brass tubes about one centimeter in diameter and ten centimeters long, and blackened on the inside, are mounted vertically in blocks for reading the mercury thread. Parallax may also be eliminated by placing the thermometer on a mirror and bringing the eye to such a position that the end of the thread and its image coincide. For very accurate calibrations short focus reading telescopes are provided. MERCURIAL THERMOMETRY 15 Procedure, Calibration of a Thermometer. The calibration consists in recording the length of a thread of mercury about ten degrees long, throughout the entire length of the capillary. Since the volume of the thread remains constant, a change in its length at any point of the capillary indicates an irregularity in the diameter of the bore at that place. From the variation in length of the thread throughout the tube, a complete plot of the form of the bore can be deduced. The first operation consists in clearing the capillary of the mercury which partially fills it at ordinary temperatures*. To do this, allow the mercury to run up into the small bulb at the top of the capillary until it is partially filled. Then, holding the thermometer in a nearly horizontal position, give the upper end a quick, light tap with a small block of soft pine wood. The thread will usually break and the mercury can then be separated into two parts, one partially filling the bulb at the top, and the other filling the true thermometer bulb, leaving the whole length of the capillary clear. Care should be taken not to allow the upper bulb to become completely filled with mercury, as under these circumstances it is often difficult to get the mercury down again into the bulb proper. The next step is to break off a thread of suitable length for calibration from the mercury in the large bulb. This is a deli- cate operation, and an unskilled manipulator is likely to crack the thermometer at the point where the stem is joined to the bulb. Students should first observe an instructor separate a thread before undertaking to do it themselves. The procedure is as follows: Hold the middle of the thermometer in the fingers of the left hand and tap the upper end sharply with a small piece of soft wood until a thread of suitable length is ejected from the bulb into the capillary. Often several small threads of mercury can be separated and afterwards joined together to the proper length. Several trials are usually necessary. Next carry the thread to the upper end of the stem by gently jarring the thermometer in an inclined position against the fingers or hand supporting the upper end. It is much safer to do this at the start and to work the thread down rather than 16 NOTES ON PHYSICAL LABORATORY EXPERIMENTS up the stem during the calibration; for there is little danger of the mercury in the small bulb at the top running out and join- ing the thread, whereas with well boiled-out thermometers this is very likely to occur with the mercury in the large bulb if the thread is being worked up the capillary. The thermometer should be handled only at its extreme ends during all of the following manipulation in order to avoid local heating of the capillary which inevitably produces apparent irregularities. In the finest work the thermometer should not be handled at all during calibration, but manipulated from a distance and read by a telescope. Starting with the thread at the extreme upper end of the thermometer, read the position of its upper and lower ends, j and 2 , respectively, to 0.1 (a good observer can estimate to 0.05). Record the observations in two vertical columns, leav- ing room for a third column for the values a-^-a^ etc. Next jar the thread slightly so that it moves down the capillary a few tenths of a degree and record the position of its ends again, of i, a' 2 - This second observation serves simply as a check on the first, for if the observations have been made with care the lengths 0,^-0% and a\-a f 2 should agree, for it is quite improb- able that the diameter of the capillary changes by an appre- ciable amount in the length of a fraction of a degree. Next move the thread about one-half its length down the stem and record the position of both ends, checking these ob- servations as before by a second observation with the thread a fraction of a degree further on in the capillary. It is un- desirable that the end of the thread should fall under a gradu- ation, as the accuracy of estimation is less in this position than in any other, on account of the width of the graduations. Proceed in this manner throughout the whole length of the capillary to below the zero graduation. Compute all the differences, a^-a^ etc., before joining the thread with the mercury in the bulb. If any large irregularities are found, carry the thread back to that part of the capillary and explore by intervals of say one or two degrees, instead of half the length of the thread, in order to locate exactly where the ir- regularity occurs. MERCURIAL THERMOMETRY 17 The mercury in the top of the thermometer can usually be readily rejoined with that in the bulb by attaching a short, stout string through the small loop in the end of the ther- mometer and swinging the thermometer in a circle. The centrifugal force expels the mercury. This procedure is always effective, provided the upper bulb is not completely filled with mercury. If this is the case, it is often difficult to connect the mercury, as a minute quantity of air in the capil- lary will prevent a thread run up from the bulb from, joining the mercury at the top. The mercury can sometimes be made to flow down into the bulb by jarring the thermometer, but more frequently it is necessary to expel a portion of it from the small bulb by heating the upper end of the thermometer above a flame. If the bulb can be thus partially emptied of its mercury contents and the remaining mercury allowed to contract in ice, this portion can then be ejected by whirling the thermometer as described above. Determination of the Scale Unit. To determine the value of this quantity the reading of the thermometer in steam, fol- lowed by its reading in ice, must be known. First. Steam Reading. The apparatus for taking the steam reading is shown in figure 2. The thermometer is sus- pended by means of a section of a rub- ber stopper fitting it tightly several de- grees above the 100 mark, which rests upon a perforated stopper closing the top of the heater. The whole thermom- eter should hang in the inner steam jacket of the boiler as shown, the bulb being an inch or two above the surface of the boiling water. The bulb should not be immersed in the boiling water itself for the following reason: If the water contains impurities, its boiling point is slightly raised, which would of course cause the "steam reading" to be 18 NOTES ON PHYSICAL LABORATORY EXPERIMENTS too high. If, on the other hand, the bulb comes in contact only with the vapor rising from the water, the vapor condenses on the thermometer and forms a coating of pure water on the bulb, the temperature of which does not rise above the true boiling point of the pure water. The water should boil briskly, but not so violently as to spatter upon the bulb. Clean tap water may be used, although distilled water is preferable. When the water has boiled for five minutes or more, raise the thermometer just high enough to read the mercury column, and record the temperature. Record the steam reading again several times and take the mean as the best representative value. The thermometer should then be carefully removed from the heater and allowed to cool in the air to about 40 C., when it should be plunged into the ice bath* and the "lag ice reading" taken. The reading of the barometer should also be recorded, from which the true temperature of the steam may be found in the steam tables. Second. The Lag Ice Reading. While the water is com- ing to a boil in the preceding operation, prepare a can, of a liter or more capacity, full of very finely crushed ice. The ice should be crushed especially fine if it has been artificially pre- pared or the weather is very cold, as under these circumstances its temperature is likely to be considerably below zero. The ice must be clean and pure. Add enough ice water to nearly fill the can. The upper layer of ice should look white. For work to 0.1 C., tap water may be used. For exact work dis- tilled water must be used. The bulb of the thermometer must be clean; the presence on it of any impurities soluble in water may lower the temperature in its immediate surroundings very appreciably. Make an opening in the ice for inserting the thermometer, with a clean glass rod. When the temperature of the thermometer has fallen to 40 C., plunge the thermometer into the ice bath fully to the zero mark, and record readings, every half minute for five minutes or more. The lowest reading is to be taken as the "lag ice reading." With thermometers reading to only 0.1, the "lag" reading does not usually change appreciably during MERCURIAL THERMOMETRY 19 the first ten minutes or so that the thermometer is in ice. With more sensitive calorimeter thermometers the immediate rise of the zero is very evident. This completes all data necessary for computing the scale unit. Computation. The computation of this experiment consists first, in the calculation of the calibration corrections of the thermometer and the construction of a plot of corrections, and second, in the calculation of the value of the scale unit. First. Calibration Corrections. Construct a plot with values of the length of the calibrating thread a-^-a^ a\-a' 2 , etc., as ordinates and corresponding values of the position of the lower end of the thread a 2 , a' 2 etc., as abscissae. The scale of ordinates should be such that the precis on of plotting will not be greater than ten times that of the data. For abscissa, a scale of I" = 10 is suggested. The best representative line should be a smooth curve passing among the points, and not a broken line. This curve will give a graphic representation of the irregularities of the capillary. The ordinate corresponding to any abscissa is the length which the calibrating thread would have had in the capillary if its lower end had been placed at the position corresponding to the abscissa in question. It is now desired to ascertain what any given reading of the ther- mometer would have been if the bore had been uniform throughout instead of irregular; in other words, what cor- rections must be applied to any observed reading in order to reduce it to the true reading of a perfect thermometer of uni- form bore. To determine this we first proceed to determine a series of consecutive "equal volume points" corresponding to the volume of the mercury thread chosen for calibration. Sup- pose we start with the lower end of the thread at any position A, near the lower end of the bore; its length in that position will be given by the ordinate y 1 of the calibration curve corresponding to the abscissa A. Its upper end will therefore read A -\- y^ If this thread be now supposed moved along the tube until its lower end stands at A -\- y lf its: 20 NOTES ON PHYSICAL LABORATORY EXPERIMENTS length will then be the value of the ordinate y%, corresponding to the abscissa A + y 1 of the curve, and its upper end will therefore read A + y\ + 2/ 2 . In this way we can determine the readings A, A + 1/1, A + y l + y 2 , etc., of a series of points which mark off, consecutively, equal .volumes along the tube. If the capillary were perfectly uniform, these points would be equally spaced. Make a four column table. Record in the first column the reading A, which in this case should be taken a few degrees below zero. The zero itself is often a convenient starting point if no temperatures below zero are to be corrected for calibration. Record in column II the ordinate y l corresponding to A as read off to hundredths of a degree from the plot. Note that rejection, in the computation, of figures in the hundredths place may result in an accumu- lated error of one or more tenths of a degree. Record in this way a series of equal volume points to above the 100 division. Let the last equal volume point nearest to and just above 100 be J5, and suppose there are n equal volume intervals between A and B. The average length of the thread y. m between the points A and B will then be y IH = - m L II. III. IV. A yi A A - A = Q A + yi y-i A + y, n A + y m (A + yi) A + yi + 2/2 y A + 2y, A + 2y jn (A + y l + y 2 ) A + yi + . . . + y n = B A + ny m = li />' B If, therefore, the capillary had been uniform in cross section throughout, and we had started with a thread of the length y, H with its lower end at A, the equal volume points between A and B would have been A, A + y m , A + 2?/ /w , etc., the last point falling at A + ny in = B. Record these values in column III. The difference between the actual equal volume points, column I, and the calculated equal volume points for a perfect thermometer, column III, is due to the irregularities in MERCURIAL THERMOMETRY 21 the bore, and represents the corrections which must be added to the actual readings in order to reduce them to the true readings of a perfect thermometer. These corrections are to be recorded in column IV. The correction for any inter- mediate reading on the thermometer may be obtained by inter- polation on a plot of corrections, which should be constructed with values in columns I and IV as abscissae and ordinates, respectively. This curve may conveniently be drawn on the same sheet with the calibration plot. Note that the numerical value of the corrections depends on the points which are selected for A and B, as their value de- termines the cross section of the imaginary uniform tube to which the corrections are referred. This makes no difference, however, in the value of the final reduced temperature, as this latter further involves the value of the scale unit (see next paragraph), which depends upon the ice and the steam reading, corrected for calibration from this same plot, and which varies, therefore, in a corresponding manner. Second. Value of the Scale Unit. Let t' s = mean steam reading corrected for calibration by preceding plot, t'i = lag ice reading corrected for calibration, t = actual temperature of steam at time steam read- ing was observed. Then the mean value of one scale unit of the thermometer in degrees is 1 The value of t may be computed from the -formula t = 100 + /o (H 760) where H is the reduced barometric reading in millimeters. The value may also be found by interpolation from suitable tables. (See Appendix or Landolt and Bornstein, Physikalisch- Chemische Tabellen, p. 60). 22 NOTES ON PHYSICAL LABORATORY EXPERIMENTS MERCURIAL THERMOMETRY PART II USE OF A MERCURIAL THERMOMETER AND DETERMINATION OF THE BOILING POINT OF A LIQUID Methods of Using a Thermometer. In order to obtain the true temperature corresponding to any observed reading of a mercury thermometer, it is necessary that a definite procedure be followed in the manipulation, and that the several errors affecting the indications of the thermometer be corrected for in a definite sequence. There are two methods of using a thermometer which depend primarily on the determination of its zero or ice reading, which, as has been pointed out, is a con- stantly varying quantity. These methods will be referred to as the "ordinary" and "lag methods," respectively. The Ordinary Method. In the ordinary method the ice reading is taken immediately before the temperature which is to be determined; it also precedes the steam reading in the determination of the scale unit, p. 21. Little or no attention is paid to the lag except by expert observers. In other re- spects this method is the same as the lag method. It is liable to errors of 0.1 C. to 0.5 C. between and 100, and is there- fore not to be followed in accurate work. The Lag Method. In this method, which is the only one by which the full accuracy of which a thermometer is capable can be attained, the ice reading is taken in every case immedi- ately after the temperature measurement. The "lag reading," i.e., the lowest temperature observed \vhen the thermometer is cooled rapidly from the observed temperature to zero degrees, is taken as the ice reading. It is sometimes called the "maxi- mum depressed zero," or "depressed zero." For work accurate to 0.1 C. to 0.2 C., the lag reading may be taken some time before or after the actual temperature measurement itself, by heating the thermometer to about this temperature and cooling rapidly to zero. The elapsed time must not, however, be so great that the zero, meanwhile, may have changed by more than the experimental error. The law expressing the relations MERCURIAL THERMOMETRY 23 between the lag at 0, and the temperature interval through which the instrument has been cooled, will be found in Guil- laume's Thermometrie. Stem Exposure. One other precaution must always be ob- served in temperature measurement whenever the whole ther- mometer, or at least the whole mercury thread, is not exposed to the same temperature as the bulb. For if the bulb is above the temperature of the major portion of the mercury thread in the stem the thermometer will evidently read too low, and con- versely. The correction is known as the stem exposure correction, and can be computed approximately if the number of degrees of mercury in the exposed stem and its temperature is known. The latter is determined by surrounding the exposed part of the thermometer with a water jacket, the temperature of which is determined by an auxiliary thermometer. A convenient arrange- ment for this purpose is a glass tube closed at the bottom by a perforated rubber stopper through which the thermometer passes, as shown in figure 3. The stem exposure correction is computed as follows : Let t' = observed apparent temperature of bulb corrected for calibration, t a temperature of the stem as determined by auxiliary thermometer, n = number of degrees exposed at tempera- ture t a , 0.000156 coefficient of apparent expansion of mer- cury in glass, t b = true temperature of bulb (desired). Then the reading of the thermometer corrected for stem exposure will be FI * 3 t" = t f + 0.000156 (t b t a ) n. As t b is really unknown we use its approximate value t' with- out appreciable error, and write //' = t' + 0.000156 (If t a ) n. 24 NOTES ON PHYSICAL LABORATORY EXPERIMENTS It is easy to see that at 100 the correction may amount to 1 C. It is a source of error too often neglected in work of even moderate precision. Order of Application of Corrections. Suppose that the ther- mometer used has been calibrated and a plot of corrections determined, and that the value of its scale unit is known. A temperature is subsequently determined as described above, the proper data for the exposed stem correction, as well as the lag ice reading, being observed. The true temperature corre- sponding to such data is then computed as follows, the correc- tions being applied in the order indicated : Let t = observed temperature of the thermometer, t a = observed temperature of exposed stem, n = number of degrees exposed at temperature t a , ti lag ice reading, a = value of one scale unit. First. Calibration Correction. Correct the observed tem- perature for calibration by means of the plot of calibration corrections. The correction taken with its proper sign should always be added. f = t + c. Second. Stem Exposure Correction. f = t f + 0.000156 (tf t a ) n. Third. Lag Ice Reading. i> -- f _ t . . Fourth. Reduction to Degrees by Value of Scale Unit. t" =i a t'". Fifth. Reduction to Hydrogen Scale. This last correction may be omitted, although if the kind of glass of which the ther- mometer is constructed is known, the correction may be readily obtained. To determine the correction experimentally a direct comparison of the mercury and hydrogen thermometer would be necessary. The amount of this correction for various kinds of glass is given in the following table, taken from Guillaume's Ther- mometrie : MERCURIAL THERMOMETRY 25 ALGEBRAIC EXCESS OF READING ON SCALE SPECIFIED OVER THAT OF THE HYDRO- GEN THERMOMETER. Scale. 10 20 30 40 50 60 70 80 90 Nitrogen . . . +0006 +0.010 +0011 +0.010 +0.009 +0.005 +0.001 0.002 0.003 Verre dur . . ; +0.052 j +0.085 +0.102 +0.107 +0.103 +0.090 +0.072 +0.050 +0.026 French crystal (hard) ... +0.064 +0.107 +0.130 +0.138 +0.134 +0.119 +0.097 +0.069 +0.036 French crystal j (ordinary) . . +0.067 +0.112 +0.137 +0.147 +0.144 +0.130 +0.107 +0.076 +0.041 Jena glass 16 +0.057 +0.093 +0.113 +0.119 +0.116 +0.102 +0.083 +0.058 +0.031 Jena glass S9 +0.024 +0.036 +0.037 +0.033 +0.026 +0.016 +0.007 +0.001 0.002 English crystal (Wiebe) . . . j o.ooo +0.02 +0.03 0.00 0.03 Fig. 4. Object. The object of the following experiment is to give practice in the proper method to follow in exact mercurial thermometry. The procedure is illustrated by the determination of the boiling point of some liquid. Apparatus. The student is to use the thermometer which he has calibrated. The apparatus required is shown in figure 4. A is a small boiling flask provided with a side tube B, which is connected with a return condenser C. The flask is clamped in position on an asbestos and wire gauze sup- port, so constructed that the direct flame does not come in contact with the flask. The thermometer is held in place by a cork fitting the neck of the flask; the bulb 26 NOTES ON PHYSICAL LABORATORY EXPERIMENTS should be wholly immersed in the liquid. The addition of glass beads, garnets, or scraps of platinum to the flask is frequently necessary to insure quiescent boiling. The exposed stem of the thermometer is provided with a stem exposure tube filled with water, the temperature of which is determined by an auxiliary "General Use" thermometer. The student will be given a liquid whose boiling point is to be determined. Procedure. First. The flask should be about one-half filled with the liquid to be investigated. 'Arrange the stem exposure tube and thermometer as shown in the figure. Bring the liquid to brisk but not violent boiling. The vapor should be completely condensed in the condenser; if this is not the case the boiling point of a solution will not be constant, but will continually rise owing to the gradual increase in its con- centration. Allow the liquid to boil for five minutes or more, during which time prepare an ice bath for the determination of the lag ice reading. At the end of five minutes record four or five readings of the thermometer and take their mean. Record also the temperature t a of the water surrounding the exposed stem as indicated by the auxiliary thermometer, and also the number of degrees of mercury thread exposed at this temper- ature. The reading of the barometer and its attached ther- mometer should also be recorded. Second. Turn out the gas, remove the thermometer from the flask and allow it to cool in the air to about 40. Then de- termine the lag ice reading as already described on p. 18. Computation. Compute the true boiling point of the given liquid, stating the reduced barometric pressure at the time of the experiment. Problems. 1. How many degrees of a thermometer may be exposed at a temperature of 20 C. with its bulb at 100 C., and the stem exposure correction be less than 0.1 C.? 2. What will be the error resulting from neglecting the stem exposure correction of a thermometer reading 300 C. with 200 of the stem exposed at temperature of 20 C. ? AIR THERMOMETRY 27 AIR THERMOMETRY Object. This experiment illustrates the use of the air ther- mometer for temperature measurement or for the determina- tion of the coefficient of expansion of a gas. The boiling point of water under atmospheric pressure is to be determined, assum- ing the value of the coefficient of expansion of the air in the thermometer known. Apparatus. The apparatus provided is a constant volume air thermometer consisting of a thin glass, spherical (or cylin- drical) bulb A blown at the end of a capillary tube B, which is bent in the manner shown in figure 5. The other end of the capillary is connected to a glass T tube C, about one centi- meter in diameter which is sealed into a three way steel stop-cock S, by means of wax. This cock is connected by heavy rubber pressure tubing to a second glass tube D, of the same in- ternal diameter as C. Both C and D are fixed to movable slides which can be clamped at any desired height along the vertical support H. The height of D may be further adjusted by means of a fine adjust- ing screw E. A scale Fjg 5 g r a d u a t e d in milli- 28 NOTES ON PHYSICAL LABORATORY EXPERIMENTS meters is attached to the front side of the support H. The height of the mercury column in C and D is read on this scale by means of a cathetometer or reading telescope. The three way stop cock S requires further explanation. Its construction will be seen from figure 6. 1 is a vertical section; 2, a front view of the cock in the same position when it is closed. It is seen that the through boring is in the direction of the handle of the cock, and the lateral boring at right angles to this direc- tion. This is indicated on the cock by the marked or flattened side. The only positions in which the cock is closed is when the handle stands at 45, as hi 1, 2 and 5. 3 is the proper position for putting C and D into free communica- tion; 4 is the position for filling the thermometer with dry air, and for drawing off the mercury from C. The boiler consists of a double walled vessel of copper in which the vapor of the boiling liquid circulates up around the bulb and down between the inner and outer walls, thus pre- venting direct radiation from the outside walls on to the bulb of the thermometer. A slotted screen M protects the mer- cury columns from the direct radiation of the boiler. Procedure. First. To fill the thermometer with pure, dry air. (This operation may be omitted if the instructor states that the apparatus is already properly filled.) Lower the bulb into the heater and bring the water to a boil. Lower D below the level of the mercury in C, and then open the stop-cock S, so that the mercury in C flows back into D until the horizon- tal opening of the stop-cock S is clear. Connect this with a T-tube, one end of which is attached by means of rubber tubing to the drying apparatus, and the other to an air pump, as in figure 7. Both of the rubber tubes should be provided with independent pinch cocks, P 1 and P 2 . The drying appa- ratus should be so arranged that fresh air is drawn through a strong solution of caustic potash or soda lime, to remove car- bonic acid, then through several dehydrating agents, such as AIR THERMOMETRY calcium chloride or strong sulphuric acid, arid finally over phosphorous pentoxide. While the water is boiling, pump the air from A through P x , P 2 being closed. Then close P l and gradually open P 2 , allowing dry air to be drawn into the appa- ratus. Close P 2 and open P x . Repeat the above operation a dozen times or more. After the last filling allow the bulb to cool to room temperature before disconnecting the drying apparatus. Then turn the stop- cock S, so that C communicates freely with D, and raise the latter until the mercury appears in C. The thermome- ter is now filled with dry air at ap- Fiff 7 proximately atmospheric pressure and room temperature. Second. To determine the pressure when the gas occupies a definite reference volume at a known temperature, the melting point of ice. This operation in gas thermometry corresponds to the determination of the zero point of a mercurial ther- mometer. Crush enough ice to fill the inner cylinder of the heater. Cover the wire bottom of the cylinder with about an inch of ice; then lower the thermometer bulb into it until the capillary stem rests on the bottom of the slot in the side of the heater. During this operation be sure that S is closed, otherwise the mercury will run over into the bulb. If this should occur, speak to an instructor. Care must be taken to exert no press- ure on the bulb, otherwise the thermometer is likely to snap off at C. Pack the bulb and stem of the thermometer with ice, filling the inner cylinder completely. Cover the top of the ice with a piece of felt or flannel to prevent circulation of air currents. Place the cover on the heater and allow the appa- ratus to stand at least ten minutes before taking any readings. A thermometer T should, in the meantime, be suspended along the vertical support H with its bulb close to C, in order to obtain the temperature of the air and mercury in C, both of which are assumed to be at the same temperature. 30 NOTES ON PHYSICAL LABORATORY EXPERIMENTS While waiting for the air to cool to 0, record the height of the barometer and its attached thermometer. After about five minutes open the stop-cock S cautiously, so that C and D freely communicate, and adjust the height of D so that the mercury in C just comes in contact with the point of the black glass reference mark. The adjustment should be made with a rising meniscus. If the mercury column now remains at rest for several minutes (the cock S being open), the air in the bulb may be assumed to have reached a constant temperature, and the height of the mercury columns in C and D should be recorded. This is to be done by means of a reading telescope provided with a horizontal cross hair. The field of view must include both the mercury meniscus and the graduated scale. Estimate readings to 0.1-0.05 mm. For very accurate work, (readings to 0.01-0.02 mm.), the eyepiece of the telescope must be provided with a filar micrometer, or a ca the tome ter must be used. Repeat the adjustment and observations two or three times and take the mean of the readings in computing the final pressure. Record the temperature ^ of the ther- mometer T. As long as the mass of air in the bulb remains unchanged, the reduced pressure p oj corresponding to this data, will be the same whenever the air is cooled to C. and the volume is adjusted so that the mercury in C stands at the reference mark. For a given thermometer containing a constant amount of gas, this pressure p<> is a constant. It is always well, however, to determine the pressure corresponding to the ice reading prior to a temperature determination in order to elimi- nate possible errors arising from leakage or change of volume of the bulb. Third. To measure an unknown temperature. To measure any temperature with a given air thermometer for which /> has been determined as above, it is only necessary to find the pressure which will bring the gas to the original reference volume when heated to the temperature in question. The method and procedure is to be illustrated by determining the boiling point of water (or any other liquid provided), under atmospheric pressure. Close the 4 stop-cock /S. Light the AIR THERMOMETRY 31 under the boiler, which should be filled with water to a depth of three or four centimeters. Tap water is sufficiently pure for this experiment, although for work of extreme accuracy, dis- tilled water should be used. The ice need not be removed from the heater unless it is desired to save time, as the steam will quickly cause it to melt and run back into the boiler. While waiting for the ice to melt, again record the reading of the barometer and its attached thermometer. When the ice has melted and the water has boiled briskly for five minutes, raise D about twenty centimeters and carefully open S. Adjust the height of D until the mercury in C comes exactly to the refer- ence mark. Wait several minutes to see if the pressure remains constant; if so, record the position of C and D as before. Re- adjust two or three times and take the mean of the readings. Record also the reading t% of the thermometer T. Finally close S, turn off the gas and raise the thermometer out of the heater. Fourth. To determine the stem exposure correction. If a portion of the stem of a mercurial thermometer is at a different temperature from that of the bulb, a stem exposure correction (p. 23) has been shown to be necessary. A similar correction is also necessary in the case of an air thermometer, due to the fact that the air in the stem and in C is not at the same tem- perature as that in the bulb when the latter is placed in ice, steam, etc. The amount of this correction depends upon the ratio of the volume of air contained in C and the stem, to the volume of the bulb. A comparatively rough determination of this ratio suffices to compute the correction with sufficient accuracy. The volume of the exposed stem is usually made as small as possible, so that the resulting correction shall be small. The volume V of the bulb is to be computed from three measure- ments of its circumference (or diameter), taken in planes at right angles to each other. The circumference may be measured with a tape, or better by a strip of paper, the length of which is afterwards measured on a scale. In work of extreme accuracy the volume may be determined by filling the bulb with water or mercury and weighing. The volume of the 32 NOTES ON PHYSICAL LABORATORY EXPERIMENTS capillary which extends into the heater may be neglected in comparison with the volume of the bulb. To determine the volume v of the air in C above the mer- cury, and of the capillary outside of the heater, raise D above C and carefully open S into position 3, until the mercury com- pletely fills C and the capillary, up to the point where it enters the heater. Close S as in 5, figure 6. Finally turn the cock into position 4 and allow the mercury to run out into a previously weighed small beaker until the meniscus just reaches the reference point. From the weight of this mercury the volume v may be at once computed. Weighings to one per cent, are sufficiently accurate. Fifth. On completing the experiment be sure that the apparatus is left as follows: C should be raised so that the bulb is out- of the heater. The mercury in C should stand two or three centimeters below the reference point, to prevent its soiling the inside of the tube where the readings are taken. The stop-cock S should be closed, and D raised above C, so that there may be no tendency for air to leak into the appa- ratus at the cock S. Computation. The temperature of the steam is to be com- puted from the data obtained. By the combined laws of Boyle and Gay-Lussac we have for a perfect gas, and practically also for hydrogen, oxygen, nitrogen, and air, PPt PoV (1 + at) (1) where a is the coefficient of expansion of the gas and / is its temperature expressed in degrees centigrade. If v = r tj we have, solving the equation for /, t= Pt ~ Po (2) ap from which t may be computed at once when the pressure p at zero degrees, and the pressure p t at /, together with the co- efficient of tension a- (equal practically to the coefficient of ex- pansion) of the gas is known. For dry air a 0.003670. This simple formula does not apply exactly, however, to the AIR THERMOMETRY 33 data taken in the preceding experiment, for the condition v = r t is not exactly fulfilled; i.e., the total mass of gas is not brought to the same^ volume at and at t, for the follow- ing reasons: First, the volume of the bulb increases when heated from to t, owing to the expansion of the glass; and second, the exposed portion of the air in C and in the capillary does not occupy the volume it would if it were brought to and t, respectively. It is necessary, therefore, to obtain correct ex- pressions for v and v t and to substitute them in the general formula (1) before solving for t. Let HI, H% = the reduced barometer readings at the time of ice and steam readings, respectively; hi, /z-2 = the mean manometer pressures reduced to 0, com- puted from the observations taken at the temperature of ice and steam, respectively; ti, t 2 = the temperature of the mercury columns at the time of taking the ice and steam readings, respectively; V the computed volume of the bulb, which may be assumed with sufficient approximation to be its volume atO; x the volume of exposed stem; k = the mean coefficient of cubical expansion of glass, 0.000027 per degree centigrade. The height hi of the mercury column DI Ci reduced to is * - 1 + 0.000181*! (Di Ci) (1 0.000181*!) approximately. Note that this may be negative, which means that the pressure of the gas at is less than one atmosphere. Similarly h 2 = (D 2 C 2 ) (1 0.000181 / 2 ) approximately. As the quantities D and C are mean results of observations taken to one-tenth of a millimeter they should be carried in the 34 NOTES ON PHYSICAL LABORATORY EXPERIMENTS computation to hundredths of a millimeter. It will be seen that the reduction to affects only the last two places of sig- nificant figures in h, hence three significant figures in the com- putation of the correction term are sufficient. The final reduced pressures p and p t are p = H l + h 1 p t = H 2 + ^2- We have next to determine the true volume v and v t which the air would have occupied if it had all been at and t, respectively. The air in the exposed stem of volume v at tf and pressure p would have occupied the volume -i ; - at 1 -}- ati and pressure p . Hence the total volume which the air in the thermometer would have occupied at is v = V + 1 + at, ' Similarly, a volume of air v in the exposed stem at t 2 and pressure p t would, at t and under the same pressure p t , have occupied the volume ^ , - (1 + at). If the volume of the bulb is taken as V at 0, at t it will be V (1 + kt). Hence the volume which the total mass of air would have occupied at t and pressure p t is Substituting these values in equation (1) we have [V (1 + *0 + r i-J = p. (V + T ^--) n + at). V Dividing by V (I + at) and putting r =p-for brevity this equation becomes l + kt , l\ ( 1 * r= r AIR THERMOMETRY 35 Solving for t apoil + 1 + at a Pt I + at 2 (apo _ kpl) r kp, (3) If ti does not differ much from t 2 , so that without introduc- ing an error greater than the experimental error they may be assumed equal, this formula reduces to t = Pt Po i i r ! + *, np kp t r a . 1 + a/! ap - kp t (Pt Po) (4) The form of the correction factor in brackets can be further simplified by writing it in the approximate form 1 + a/! ap kp t If, in this correction term, kp t can be neglected in compari- son with ap Q , the correction further simplifies to 1 + ,^-r^, 1 + a/j p and equation (4) becomes Pt ap kp t 1 + 1 + (5) Notice that formula? (4) and (5) reduce at once to (2) if the 7) stem exposure correction involving -- = r and the correction for the expansion of the bulb, kp tj are negligible. Coefficient of Expansion of a Gas. If instead of solving for t, this is known, the above data may be used for determin- 36 NOTES ON PHYSICAL LABORATORY EXPERIMENTS ing a, the coefficient of expansion of the gas. Inspection of equation (3) will show that the equation contains a in three places in such a way that a general solution is exceedingly laborious. Since a enters only in small corrections factors in the terms _ - and _ we may assume an ap- 1 + a/! I + at 2 ' proximate value for it in these terms and solve for a in the term at. If the value thus obtained differs too widely from the assumed value of a, a second or even third approximation must be made. One approximation usually suffices. Solving for a in (3) under this assumption we obtain If /! and # 2 are so nearly the same that they may be assumed equal, this equation becomes a = or simplifying the correction factor by an approximation, 1 4- /, Problems. 1. How precise should the ratio ~= r be determined in this experiment in order that the resulting devi- ation in t (formula 5) shall not exceed 0.3 per cent? 2. What precision in v and V does this correspond to in the actual apparatus used? 3. How precise should a (formula 5) be known for a pre- cision of 0.3 per cent in t, assuming other sources of (jrror negligible? PRESSURE AND BOILING POINT 37 PRESSURE AND BOILING POINT, AND PRESSURE OF SATURATED VAPOR Object. This experiment is designed to study the change of the boiling point of a liquid under varying pressure, and to illus- trate the dynamical or boiling-point method of determining the pressure of saturated vapor at different temperatures. The ex- periment also furnishes data for illustrating the application of the fundamental thermodynamic formula for the liquid-vapor state to the calculation of the specific volume of saturated vapor. Discussion. A pure liquid can exist in equilibrium with its vapor at any definite temperature and one corresponding pressure, or conversely at any definite pressure and one cor- responding temperature. If at any temperature the external pressure on a liquid is greater than the pressure of its vapor and the temperature of the liquid be gradually raised, the pressure of the vapor will increase until it is exactly equal to the external pressure when the liquid will begin to boil. The pressure at which a liquid boils is therefore a direct measure of the pressure of its saturated vapor at its boiling point, and the determination of the boiling point of a liquid under dif- ferent pressures affords an excellent method for the investigation of the pressure of saturated vapor at various temperatures. This is known as the Dynamical Method of vapor pressure measure- ment as distinct from the Statical Method, in which the liquid is introduced into the top of a barometer maintained at a known temperature and the depression of the mercury column observed. The Dynamical Method is by far the more accurate, as it is but little affected by slight impurities in the liquid. The Statical Method, on the other hand, is liable to grave errors from this source, particularly if the impurities are very volatile. The only rigid relation holding between the pressure p and the boiling point t of a liquid, or in other words, between the temperature t and the pressure p of its saturated vapor, is the thermodynamical equation 1 Introduction to Physical Science," p. 161. dt _ a see anv work on Thermodynamics, a: 95; Noyes' i For deduction of this formula see any work on Thermodynamics, as Clausius "Mechanical Theory of Heat," p. 129; Peabody's "Thermodynamics," p. 38 NOTES ON PHYSICAL LABORATORY EXPERIMENTS where r is the latent heat of vaporization of the liquid at t C., T the absolute temperature corresponding to t C., and v^ and v 2 , the corresponding specific volume of the liquid and its saturated vapor, respectively. As these last quantities as well as r are functions of the temperature, the above equation cannot be integrated without making simplifying assumptions, or by the aid of empirical relations between the quantities r, Vi, v 2 and the temperature t. Thus for water, Clausius de- duces from Regnault's measurements the following empirical formula for r: r = 607 0.70&. The exact way in which t' 2 varies with t, i.e., the form of function v 2 = / (t) is known for only a few vapors. Sat- urated vapors are often assumed to follow Boyle's law, i.e., 7? T v 2 = , but this assumption is in most cases only a rough approximation and is liable to lead to erroneous results. Equation (1) is of great value in computing the specific dj) volume v 2 of saturated vapor when -^- and r are known, as r 2 itself can be experimentally determined with accuracy only with great difficulty. The specific volume i\ of the liquid is approximately equal to unity, and therefore is usually negligible compared with v z in any computation. The experimental determination of -5- affords therefore a valuable means of find- ing indirectly the specific volume of saturated vapor. Equation (1) is not limited to changes from the liquid to the vapor state, but holds equally true for all changes of state, for example the melting of ice to water, in which case r denotes the latent heat of fusion, T the absolute melting point, i\ and r a the specific volumes of the substance in the initial and final states respectively. Besides the thermodynamic formula (1) between t and p, numerous empirical relations have been proposed by different investigators. 1 Only one will be mentioned here, namely, that i Winkelmann, "Handbuch der Physik," vol. ii. 2, p. 702. Ostwald, "Lehrbuch der Allgemeinen Chemie," vol. i. p. 313. PRESSURE AND BOILING POINT 39 proposed by Regnault to represent his classical data on a large number of saturated vapors. By plotting temperatures and cor- responding pressures on a large scale, he found the resulting curves could be represented by interpolation formulae of the type log p a -f- ?7a* where a, b, and a are constants depending on the nature of the liquid, t = t c -f C, where t c is the temperature in centigrade degrees and C is a constant. He derives the following values for these constants for the following typical liquids: a b log a C Water 5.42332 5.46428 0.99723111 +20 Alcohol 5.54320 -5.01945 0.99720211 +20 Benzene 4.67667 -4.07461 0.99656761 -J-O4 Apparatus. The arrangement of the apparatus is as follows : An open manometer A is connected through a large air reser- voir B, and a return condenser C, with the boiling apparatus D. This consists of a horizontal brass cylinder in the axis of which is sealed a small brass tube closed at one end for containing the thermometer for registering the tem- perature of the boiler. The pressure in the apparatus may be varied by con- necting the reservoir #j[with a suction or a pressure pump through the bottle F. This is inserted as a trap to prevent water from the water pump from sucking back into the appara- tus, and to collect, when the cock E is opened, any water which may have condensed in B. r Fig 8. 40 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The boiler is filled with water through a thistle tube gauge attached at one end; the height of water in the boiler is indicated by the position of the water in this gauge which is of glass. The burner is constructed so as to distribute a series of small flames along the length of the boiler. Procedure. The following directions apply particularly to water, which is the liquid used in this experiment : First. Connect B to the suction-pump through the safety bottle F and exhaust until the pressure within the apparatus is reduced to about 50-60 mm. Close E and the second stop-cock between F and the pump. Then, and not before, turn off the water. See that the apparatus is air-tight (indicated by a con- stant reading of the manometer), before proceeding further. If it is not, speak to an instructor. Second. See that the waste-cock from the condenser is open before turning on the water through C. It should never be closed. f Turn on the water, so that a good stream flows through the condenser. Third. Bring the water in the boiler to brisk boiling. Only a small flame will be necessary. The boiling point will probably be not more than 15 or 20 above the temperature of the room. As soon as the thermometer indicates a constant temperature, record the temperature and the height of the mercury in the manometer. Record also the reading of the thermometer attached to the manometer, the height of the barometer, and its temperature. Usually two barometer readings, one at the beginning of the experiment and one at the end, will be sufficient, unless it is changing very rapidly, when readings should be taken directly before or after recording the manometer. This completes all data necessary for the first set of observations. Next allow air to enter the apparatus through E until the manometer indicates an increase of pressure of about 100-150 mm. By thus increasing the pressure, boiling will instantly cease until the temperature has risen to the new boiling point, when a second series of observations similar to the above is to be taken. Determine in this manner the boiling points cor- PRESSURE AND BOILING POINT 41 responding to six or seven different pressures, taking the last observation at atmospheric pressure, or a little above it. This last may be done by forcing air into the apparatus at E by means of a small force pump. Computation. Correct the observed boiling points for ther- mometric errors (see table of corrections for thermometer). Reduce the corresponding pressures in millimeters of mercury to C., assuming the manometer scale (of seasoned boxwood) to be correct at ordinary temperatures. Plot the reduced data with pressures as ordinates, and temperatures as abscissae. This will show graphically the relation between the pressure and boil- ing point of the liquid, or, in other words, the variation of the presmre of its saturated vapor with the temperature. Ca^ulate by equation (1) the specific volume of saturated steam, v 2 , at 100 C., and compare it with the value given in Peabody's Steam Tables or in Table VIII., Appendix. Note. To obtain the value of ~ at 100 where the vapor pressure curve will be seen to be nearly linear over a consider- AT? able range of temperature, compute the approximate value -j by taking two points on the actual curve near 100, instead of attempting to draw a tangent to the curve at that point. With a thermometer reading to 0.001 C., and a sensitive manom- Ap eter the value of -j can be obtained directly from the observed data on two boiling points with considerable accuracy. Remember in solving for v 2 in equation (1) that both -jr and r must be expressed in mechanical units. Problems. 1. At what pressure will an error of 0.1 mm. in p begin to affect the corresponding value of t by 0.1 C.? By 0.05 C.? (Solve by inspection of Steam Tables.) 2. Compute from formula (1) the melting point of ice under a pressure of ten atmospheres. Given : latent heat of fusion of ice 80 calories, specific volume of ice 1.09 c.cm., specific volume of water at C. = 1.00 c.cm. UNIVERSITY or CALORIMETRY GENERAL DISCUSSION This discussion should be carefully studied before beginning any experimental work on calorimetry. Calorimetry is the process of measuring quantities of heat. The process in general consists in transforming a quantity of some form of energy, as electrical energy or mechanical energy into heat energy, in a vessel called the calorimeter which con- tains water, or some other appropriate liquid, and in measuring the resulting phenomenon produced. By the principle of the conservation of energy the quantity of energy thus introduced is equal to the sum of all the energy changes resulting in the calorimeter, supposing the latter to receive no other energy from, or give no energy to, the surroundings. The various calorimetric methods devised seek to reduce these energy changes to the simplest and most accurately measurable forms. The most common method, known as the Method of Mix- tures, consists in introducing the energy directly into a calorim- eter containing a known weight of water, in which case the phenomenon to be measured is simply the resulting rise of temperature of the calorimeter and water. If this be accu- rately determined and the weight and specific heat of the water, together with the weight and the specific heat of the calorimeter and all its parts be known, the quantity of heat energy intro- duced into the calorimeter is given at once by the expression : q [ WoSo . -f 2 WtSi] A/ (1) where w and s is the weight and specific heat, respectively, of the water (s may usually be taken equal to unity), w k; s k are the weights and specific heats, respectively, of the materials constituting the various parts of the calorimeter, and A is the rise of temperature common to them all. Simple as the method is in theory the quantities involved in the measurements and the conditions to be observed are such CALORIMETRY 43 that calorimetric measurements, which are reliable to 0.1 per cent, are among the more difficult laboratory processes. Units. The unit of heat energy is the calorie, or more speci- fically the gram-calorie or kilogram-calorie. It is defined as the quantity of heat required to raise a unit mass (one gram or one kilogram) of water through one degree centigrade. It has been experimentally found that this quantity varies with the temperature, hence, in order to definitely define the cal- orie, it is necessary to further state the particular temperature to which it is referred. Owing to the choice of various temper- atures by different observers, several calories have come into use with the inevitable result of introducing great confusion in the comparison of the results of different investigators. The universal adoption of one definite unit is much to be desired; but until the use of such a unit becomes general, a definite statement of the calorie used should always be made in expressing experimental results which have any claim to accuracy. The following different calories should not be con- fused : 1. ZERO DEGREE CALORIE: The quantity of heat required to raise one gram of water from to 1 C. 2. ORDINARY CALORIE: cal. The quantity of heat required to raise one gram of water from 15 to 16 C., this being taken as the mean room temperature. 3. MEAN CALORIE OR ICE CALORIMETER CALORIE: The one- hundredth part of the heat required to raise one gram of water from to 100 C. 4. OSTWALD'S CALORIE: K. The quantity of heat required to raise one gram of water from to 100 C. 5. BERTHELOT'S LARGE CALORIE: Cal. 1000 times the ordi- nary calorie as defined above. The zero degree calorie is of little or no practical use, and is to be regarded only as a classical definition introduced by Regriault. The specific heat of water in the neighborhood of zero degrees is very difficult to determine with accuracy, and hence were this unit adopted, its value would be more uncer- tain than the calorimetric measurements themselves. 44 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The ordinary calorie denoted by cal. is that most frequently adopted, as most calorimetric measurements are carried out at "room temperature," which is variously taken from 15 to 18 C. The calorie is nearly constant throughout this range of temper- ature. The mean calorie or ice calorimeter calorie has been used chiefly in expressing results obtained with the ice calorimeter, which is usually calibrated by the quantity of heat given out by water cooling from 100 to O 6 . This unit does not differ from the ordinary calorie by more than 0.14 per cent. Ostwald, following the suggestion of Schuller and Wartha, has proposed the 100 times greater unit denoted by K, as being not only of a more convenient magnitude for expressing thermo- chemical data, but also more rational than the somewhat ar- bitrary ordinary calorie. Its advantage as a thermo-chemical unit of heat measurement will be seen from the following ex- ample: The heat of combustion of one atomic weight (12 grams) of carbon to carbon dioxide is 97000. cal., but as thermo- chemical data are seldom reliable to more than 0.1 per cent, i.e., to four significant figures, the superfluous ciphers necessary to fix the decimal point may be avoided by using the larger Ostwald calorie K, and writing the above quantity of heat 970 K. For the same reason Berthelot adopts the still larger unit 1 Cal. = 1000 cal. for expressing the results of his thermo- chemical investigations. Ostwald's calorie is in general use in Germany; Berthelot's in France. From the most recent determinations of the variation of the specific heat of water with the temperature, the following re- lations hold between the various calories above defined: 1 zero degree calorie 1.008 ordinary (15 - 16) calories. 1 1 mean calorie = 1.0014 ordinary (20) calories. 2 In absolute units 1 ordinary (15) calorie = g J ergs 980.6 X 42730 ergs = 4.190 X 10 7 ergs J 42730 gram-centimeters at sea level, 45 latitude (g = 980.6), and referred to the ordinary calorie. 1 Liidin, Wied. Beiblatter, 9O, 764, 1896. 2 Callander and Barnes, Phys. Rev., 1O, 213, 1900. CALORIMETRY 45 Sources of Error. The principal sources of error which arise in calorimetry, and which in accurate work must be corrected for or rendered negligible by special adjustment of the condi- tions of the experiment, are the following: First. Errors in Thermometry. The rise of temperature in a calorimetric measurement is in most cases small a few de- grees only hence thermometers sensitive to at least 0.01 C. are usually required. When the rise of temperature is very small, a few tenths of a degree only, thermometers indicating differences of temperature of 0.005 or even 0.001 are required. The calibration errors and scale unit of such calorimeter ther- mometers must be carefully determined, as well as the cor- rections for all other thermometers used in the work. Second. Errors arising in the determination of the heat ca- pacity or water equivalent of the calorimeter. By this is under- stood the value of the term ^w k s k in formula (1), that is, the total heat capacity of all parts of the calorimeter and its con- tents, exclusive of the water. This is called the "water equiv- alent" of the calorimeter, since this number of grams of water (specific heat unity), would be raised through the same tem- perature as the material in question by the same quantity of heat. If the weights and specific heats of all parts of the calorimeter are known with sufficient accuracy, the water equivalent can be computed at once, in which case the calori- metric measurement is a primary one. If, on the other hand, these data are not known with sufficient accuracy, the water equivalent has to be experimentally determined, and the meas- urement is then a secondary one. It is always desirable that the water equivalent of the calo- rimeter be as small as possible in comparison with the weight of water used. The material of which a calorimeter is Con- structed should therefore be as thin as is consistent with rigidity, and should have as low a specific heat as possible. It is also desirable that it have a high thermal conductivity in order to assume quickly the mean temperature of the water, and for reasons mentioned below, it should also be capable of a high polish. The metals best fulfilling these conditions will be seen from the following table: Platinum Sp. Heat 0.032 Density 21.5 Product 0.69 Silver 0.056 10.5 0.59 Nickel 0.11 8.9 0.98 Copper Glass 0.093 0.20 8.9 2.4 0.83 0.48 Mercury 0.033 13.6 0.45 46 NOTES ON PHYSICAL LABORATORY EXPERIMENTS Thermal Conductivity 109. 82. 0.13 2. It appears from the above table that silver and platinum are the metals best adapted for constructing calorimeters, both on account of their low specific heat and high thermal conduc- tivity. Platinum is the more durable, and is especially adapted for thermo-chemical experiments involving the use of acids and bases which attack other metals. Gold-plated silver calorim- eters may, however, often be used for such experiments and are much cheaper. Glass is not to be recommended on account of its very low thermal conductivity, which is only about one- thousandth that of silver. Nickel, or nickel-plated copper may be used with non-corrosive liquids. The exact computation of the heat capacity of the bulb and immersed portion of the calorimeter thermometer is usually impossible, as the weight of mercury and glass cannot sepa- rately be known. It happens fortunately, however, that the heat capacity of an equal volume of mercury and of glass is nearly the same, 0.45 and 0.48, respectively (see above table). Hence the heat capacity of the immersed portion of a thermometer may be computed with very close approximation as the pro- duct of the mean of these values, namely 0.465, times the total volume of the part of the thermometer which is immersed. Third. Errors arising from exchange of heat by conduction and radiation. As every calorimetric measurement requires time for its completion, the calorimeter and contents will gain or lose a certain quantity of heat by conduction and radiation from or to the surroundings, unless the surroundings are main- tained exactly at the temperature of the calorimeter through- out the experiment. As the temperature is continually chang- ing, this condition cannot in general be realized, and hence corrections must be made for these two sources of error. Gain CALORIMETRY 47 or loss of heat by conduction may be practically eliminated by supporting the calorimeter on three non-conducting points such as corks, or resting it on a net-work of strings. If the calorimeter could be vacuum jacketed, practically all exchange of heat by conduction or convection would be eliminated. The errors due to radiation are however more serious, and constitute one of the most troublesome sources of error met with in calorimetric work. The quantity of heat radiated (or absorbed) by a surface is proportional to: 1. The area of the radiating surface. 2. A constant depending on the nature of the radiating sur- face. 3. The difference of temperature between the surface and surroundings. 4. The time during which radiation takes place. The radiating surface should therefore be as small as is con- sistent with the required volume. Calorimeters are usually cylindrical in form, and hence for a closed calorimeter, i.e., one provided with a cover, the best relative dimensions would be height = diameter. They are usually, however, made with the diameter considerably smaller in proportion than this, in order to diminish the area of the surface of the liquid exposed to evaporation. Calorimeters of less than 400-500 cubic centime- ters capacity are not to be recommended except for special work. The numerical value of the radiation factor depends upon the degree of polish of the radiating surface. If the surface is rough and tarnished the coefficient is large, being a maxi- mum for a "perfectly black" surface. On the other hand, it may be reduced to a very small value by giving the surface of the calorimeter the highest possible burnish. To still further reduce this source of error the calorimeter should be enclosed within a second vessel or jacket whose inner walls are also bur- nished. The third and fourth factors show that the temper- ature of the calorimeter should not differ very greatly from that of the surroundings, and that the duration of the experi- ment should be as short as is consistent with other conditions. If the difference in temperature between calorimeter and sur- 48 NOTES ON PHYSICAL LABORATORY EXPERIMENTS roundings amounts to more than about 10 C., the conditions enumerated above, which are a statement of Newton's Law of Cooling, no longer hold true. In what follows it will be assumed that the temperature difference does not exceed this amount. Cooling Correction. Let us now investigate how the heat lost or gained by radiation may be allowed for or eliminated. This correction is generally known as the "cooling correction." A calorimetric measurement consists in general of the three fol- lowing continuous operations: First. Preliminary readings of the temperature of the water in the calorimeter every half minute for at least five minutes immediately preceding the operation proper. Second. The operation proper, consisting of introducing heat into the calorimeter, e.g., dropping in a hot substance as in "Specific Heat/' or passing in steam as in "Latent Heat," or heating a coil of wire by an electric current as in "Mechanical Equivalent." Third. Final temperature readings after the operation has ended, continuing at half minute intervals for at least another five minutes (better for eight or ten minutes), these data to serve for determining the final rate of gain or loss of heat. The preliminary readings furnish data for finding the tem- perature (which in general cannot be read), at the moment of beginning the operation, and for . determining the rate of gain or loss of heat of the calorimeter at that time. If the data thus obtained be plotted with temperatures as ordinates and times as abscissa?, curves of the following general type will be obtained: & Fig CALORIMETRY 49 Curve a, figure 9, represents the general case in which the calorimeter gains heat from the surroundings from A to B; the operation begins at B and heat is developed within the calorimeter until the temperature has risen to C; at C the oper- ation ceases, but if certain parts of the calorimeter or its con- tents have become heated above the mean temperature of the calorimeter, there will then result a further rise of temperature due to the equalization of temperature between such hot parts and the water of the calorimeter, or between the water and the metal of the calorimeter itself. This will be represented by the portion of the curve CD, D being the temperature at which the whole calorimeter and contents arrive at a uniform temperature. If D is above the temperature of the surround- ings, as is usually the case, the calorimeter will then give up heat to the surroundings by radiation at a uniform rate repre- sented by the straight line DE. The temperature D marks the beginning of this straight line which should be tangent to the curve CD at D. In certain operations, as in the development of heat in the calorimeter by heating a coil of wire by a current (as in "Me- chanical Equivalent"), or in condensing steam in the calo- rimeter (as in "Latent Heat") the portion CD of curve a may become very small as in curve 6, very little rise of tem- perature occurring after the operation ceases. On the other hand, when a heated mass is suddenly introduced into the cal- orimeter (as in "Specific Heat"), the whole operation consists of an equalization of temperature, and B and C fall together. In this case CD may take any form between a curve of type c and a nearly straight line, as in curve d, according to the ve- locity with which the equalization of temperature takes place. If the substance introduced is a good conductor and has a large surface compared with its mass, e.g., if it is cut up into small pieces, the curve will be of the form d. If, however, the substance is a single large mass of poorly conducting material, such as vulcanite or glass, the curve will take the form c. In order that curves similar to the above types may be ob- tained, it is absolutely essential that the stirring be so efficient 50 NOTES ON PHYSICAL LABORATORY EXPERIMENTS and the thermometer so placed in the calorimeter, that the temperature indicated is the mean temperature of the calorim- eter and contents as a whole, at the time of observation. Irregularities in the curves can almost invariably be traced to failure to fulfil one or both of these conditions. Thus a hump in the curve at D indicates that the bulb of the thermometer has been unduly heated by too close proximity to the source of heat. In all such cases the data should be rejected. Demonstration. It will now be shown how the cooling cor- rection can be computed, first for the general case represented by a, figure 9, and then for several special cases. General case. Let r l be the rate of exchange of heat of the calorimeter in degrees per minute, reckoned plus for gain and minus for loss of heat, as deduced from the tangent of the straight line best representing the temperatures between A and B. Let ^ = the temperature at the instant the operation begins at B, and &i, the corresponding time. Note that since one observer can seldom read this temperature at the time of performing the operation, it must be obtained by extrapolating the line AB to the time l7 at which the operation begins. Sim- ilarly let r 2 be the rate of exchange at the final temperature t z at the time 2 , i.e., the temperature and time corresponding to the point D. Let t a be the mean temperature of the sur- roundings. The calorimeter then gains heat from the sur- roundings up to a time O a when its temperature reaches that of the surroundings, after which it begins to lose heat. By Newton's law of cooling the rate at which a body gains or loses heat by radiation is directly proportional to the differ- ence of temperature between the body and its surroundings. Applied to a calorimeter, if its heat capacity does not sensibly vary during the operation, we may assume that its rate of loss or gain of heat is proportional to its rate of rise or fall of tem- perature. This assumption is made in the following demon- stration : Let the temperature change per unit time at any tempera- ture t be denoted by r. Then r = a (t n where a is a con- stant depending on the nature of the given calorimeter. CALORIMETRY 51 The total rise in temperature due to radiation during the interval from 1 to 2 will b e therefore r#2 Ch r C e * Ch ~i I rdO = a I (t a t) dO = a \t a I do - I tdO JQ\ J9\ [_ *J9\ , /#i = a [4, (fl, - ,) -jjp / (6) d] . (1) /*02 But I / (0) e?0 is the area bounded between the curve *J6\ the ordinates at 6 l and 2 , and the axis of 6. Its approximate value may be found by computing the mean value of the ordi- nate t m , i.e., the mean value of the temperature between t 1 and / 2 , and multiplying by the time interval 2 lt t - f- 4- 6 4- c + 4- -1 "n-lL2 2j where a, 6, ... n are temperature readings taken from the plot or data at the time 6 l and each following half minute up to 2r respectively. Hence the approximate value of formula (1) becomes rdO = a J = a (t a t m ) (0 2 ^), which taken with opposite sign is the correction due to radia- tion to be added to the observed rise in temperature. The corrected rise of temperature is therefore t 2 t 1 + a(t, H t a ) (0 2 0i). (2) This formula is general and can be applied to a plot of calori- metric data of any form. The radiation factor a can be determined at once from the simultaneous equations TI = a (t, /j) 7*2 ~ & (t(t '2) whence 52 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The mean temperature of the surroundings t a can be ob- served, or it may be computed from the above equations as ^ = t i+~ or;4=^V+ ^ It is evident from the above deduction that the correction term in (2) becomes zero when t m = t a . By preliminary ex- periments on the actual rise of temperature occurring in the experiment, it is possible to calculate what the initial tempera- ture of the water below the temperature of the surroundings should be in order that this condition may be fulfilled, and the extra labor thus involved is in many experiments warranted. Special Case I. The Rumford Method. The total rise of temperature is at a uniform rate. If the rise of temperature is uniform during the whole operation, and the part CD of the curve is negligible com- pared with BC, i.e., C and D practically coincide, the mean temperature t m will evidently be t m 1 ~}~ 2 . Hence if the initial temperature of the water is brought to just as many degrees below the temperature of the surroundings t a , as the final temperature is allowed to rise above this temperature, then t m = t a and the gain and loss of heat during the opera- tion will practically offset each other. The observed rise of temperature will therefore be the correct one. This is known as the Rumford Method of eliminating the cooling correction. It is to be especially noted that it is only applicable when the entire rise of temperature is at a uniform rate, for only then is If in the above case the initial and final temperatures are not so adjusted with respect to the surroundings that t m = t a , i.e., TI is not exactly equal to r 2 , it is easy to show that the cor- rection to be applied (i.e., added) is -^i"' (,-i). (3) CALORIMETRY 53 For suppose the data to be represented as in figure 10. If t a is the mean temperature of the surroundings, the loss of heat during the time the temperature rises from t a to t 2 will be exactly compensated by gain of heat during the in- terval it is rising from some temperature t x to t a where t x is just as far below t a as t z is above it. The resultant cor- rection will therefore be the gain of heat during the period 1 to O x while the tempera- ture is rising from ^ to t x . This may be found at once by substituting in the general formula (1). We obtain for the correction This may be written (fr- 1 T" tj: and -fnf -fllT f .r 4 ta h But (,. = t a (t 2 t a ) = 2t a hence the correction reduces at once to /*! and r 2 are obtained by finding the tangent of the angle which the straight lines best representing the preliminary and final readings, make with the axis of respectively. They are to be algebraically added, gain of heat being reckoned positive, and loss of heat negative. \ '3 R A O- THE ' UNIVERSITY or 54 NOTES ON PHYSICAL LABORATORY EXPERIMENTS Special Case II. The rise of temperature from B to C is uniform, but the portion of the curve CD, although small, is not negligible compared with BC, fig- ure 11. Then, since the rate of ex- change during the interval CD is practically r 2 , the temperature would have risen to C' had the equalization of heat from C to D been instantaneous, where C" is the intercept of DE ex- tended back to the ordinate through C. Call this temperature /' 2 . The cooling correction for the interval BC is that already deduced under Special Case I. Hence the corrected rise of temperature will be t _ y JJI /-/ /) \ 2 6 1 "2 ^ 2 ly ^ (4) the abscissa of where 0^ is the time corresponding to ' 2? the point C or C f '. Special Case III. The rise of temperature .during the oper- ation is uniform, and the initial temperature is so adjusted that r 2 = 0, i.e., DE is horizontal. This is evidently a special case of the above, and the corrected rise of temperature is t 2 ti y (0 ^ (5) Special Case IV. When the equalization of temperature CD is slow, as in c, figure 1, or constitutes a considerable por- tion of the total rise, it is advantageous to so adjust the initial temperature that the final temperature / 2 coincides as nearly as may be with the temperature of the surroundings, i.e., so that r 2 = 0. The correction is to be computed by the general formula. This procedure not only reduces the magnitude of the rate r 2 most affecting the correction, but also serves to de- termine it with greater accuracy. SPECIFIC HEAT OF SOLIDS 55 SPECIFIC HEAT OF SOLIDS THE METHOD OF MIXTURES Object. The object of this experiment is to determine the specific heat of a solid substance by the Method of Mixtures to about 0.5 per cent. The experiment illustrates the general procedure in a simple calorimetric measurement, the further application of various matters discussed under thermometry, and the method of applying the cooling correction. Apparatus. The apparatus used is shown in figure 12. It consists of an open calorimeter C of burnished nickel-plated copper which rests on cork supports inside a similar nickel plated vessel or jacket; a stirrer S of the same ma- terial is also pro- vided. The calori- meter thermome- ter 7 7 for measuring the rise in tempera- ture is held in place. by a support fixed to the jacket. The calorimeter is protected from the aa heat and the steam of the boiler by a double walled screen W open at the bottom and top to permit free circulation of air. The heating apparatus consists of a boiler B, on the top of which is placed the heater proper, H. This consists of two concentric brass cylinders joined at the top. The inner cylin- der is closed at the bottom and forms a receptacle for the sub- stance to be heated. The bottom of the larger outer cylinder terminates in a conical tube by means of which it is connected with the boiler. The steam passes up around the inner cylinder ms 56 NOTES ON PHYSICAL LABORATORY EXPERIMENTS and escapes through a small side tube at the top. The outer cylinder is heavily lagged with felt to prevent loss of heat and to facilitate handling while hot. The substance to be heated is placed in the inner cylinder which is then closed by a cork or rubber stopper, through which the bulb of the thermometer for taking the temperature of the substance should pass easily. The upper part of this thermometer which projects beyond the stopper is enclosed in a "stem exposure" tube P (see page 23) filled with water, the temperature of which is determined by an auxiliary thermometer not shown in the figure. The corrections for all thermometers used with the apparatus are given on their cases. Procedure. Place the substance in the heater and begin heating it up at once, as the longest part of this experiment consists in allowing the substance to reach a uniform high temperature. See that the graduations on the thermometer which is used for taking the temperature of the substance are distinctly visible from 90-100. If not, rub in some lead with a soft pencil. If this precaution is not observed, difficulty may be encountered in reading the thermometer afterwards when it is immersed in water. Arrange the thermometer and stem exposure tube as shown in the figure. Record where the thermometer- enters the tube as datum for determining the stem exposure correction. While the substance is heating, weigh the calorimeter and the stirrer, dry. Next fill the calorimeter to about three-fourths its capacity with water and weigh. Ordinary tap water may be used. As the exact rise of temperature is unknown, it is not possible in a single experiment to adjust the initial temper- ature of the water to the best point below that of the surround- ings. The apparatus is so designed, however, that the rise of temperature with the substances employed is about 4 or 5. Moreover the substance used is metal, and is divided into a number of small pieces so that the equalization of heat between it and the calorimeter is very rapid. The plotted data will give a curve similar to that in d, figure 1. With this knowledge it is best to adjust the water in the calorimeter to about two or SPECIFIC HEAT OF SOLIDS 57 three and one-half degrees below the temperature of the sur- roundings, i.e., the temperature indicated by a thermometer (the calorimeter thermometer may be used), placed within and touching the side of the jacket surrounding the calorimeter. If a preliminary experiment should show the equalization of temperature to take place slowly, as in the case of poorly con- ducting substances, the initial conditions should be adjusted a& described under special case IV, p. 54. A blank form should next be prepared for recording data with one column for the time in hours, minutes and seconds, and another for the corresponding temperature readings. The times should be written down beforehand in half-minute inter- vals for a period of at least fifteen minutes. Such a previously prepared blank is of great assistance in taking down data of this kind, as it lessens the labor during the operation, dis- tracts the attention of the observer less from his temperature readings, and in case any observations are omitted, greatly lessens the confusion in recording subsequent data in their proper place. When the temperature of the heated substance becomes constant, and not before, begin taking the thermometer read- ings. Record first with the calorimeter thermometer the tem- perature t s of the surroundings (inside of the jacket). Then place the thermometer in the calorimeter and with regular and constant stirring (a long and not too rapid up and down motion), begin the "preliminary readings," continuing the same for at least five minutes. The thermometer should be read to 0.01 C. Suppose, for illustration, that the first reading was at 2 h. 35 min. sec. At the end of five minutes, i.e., after the reading at 2 h. 40 min. sec., suspend readings of the calorim- eter thermometer and prepare for the operation proper. First, read the temperature of the stem exposure thermometer and remove it. Second, read very carefully the temperature of the hot substance. Third, remove the thermometer with its at- tached stem exposure tube from the heater and place it in the support R. In this operation do not remove the cork closing the heater; otherwise the substance will become some- 58 NOTES ON PHYSICAL LABORATORY EXPERIMENTS what cooled. These operations can be easily made without undue haste during the minute from 2 h. 40 min. sec. to 2 h. 41 min. sec. A few seconds before the latter minute expires remove the heater from the boiler, and exactly on the 41st minute take out the stopper and pour the hot substance into the calorimeter. The calorimeter thermometer should be so placed that the substance is poured away from its bulb, not only to prevent accident, but also to avoid local heating of the water in the neighborhood of the bulb. It is safer during this operation to raise the thermometer out of the calorimeter entirely. Immediately after the transfer resume stirring the con- tents of the calorimeter as thoroughly as possible. The success of the experiment from this point on depends largely on the efficiency of the stirring. Read the calorimeter thermome- ter one-half minute after the operation, i.e., at 2 h. 41 min. 30 sec., and on every following half-minute for eight or ten min- utes, stirring of course constantly. This completes the calori- metric observations. There still remains only to determine the weight of the substance dry. At the conclusion of the experiment replace the substance (dry), all three thermometers, and stem exposure accessories, in their case and return the same to the instructor. Computation. First. Make a plot of the temperature and time observations, and from it determine the cooling correc- tion. The form of the curve obtained will determine which method, pp. 52-54, it is best to apply. The temperature ^ of the calorimeter at the instant of inserting the hot substance is also to be determined from the plot. Second. Compute the temperature t t of the hot substance at the time of introduction into the calorimeter, applying cali- bration and stem exposure corrections to the observed reading. See p. 23. Third. Calculate the water equivalent of the calorimeter, k = w 1 s l -f- w 2 s 2 -f- . . . = 2 w^ t . The specific heat of the material of the calorimeter may be taken as 0.095. The water equivalent of the immersed thermometer is readily shown to be negligible in this experiment. SPECIFIC HEAT OF SOLIDS 59 Fourth. Compute from the above data the specific heat of the substance. The formula for computing the specific heat by the method of mixtures is (w + A:) (L ti) where 6- = specific heat of substance; w = weight of substance; u\, =. weight of water; w ly w 2 , etc. = weights of various parts of calorimeter; >?!, s 2 , etc. specific heats of various parts of the calo- rimeter; t, t 2 = corrected fall of temperature of substance ; / 2 - t l corrected rise of temperature in calorimeter. Precision Discussion. If each parenthesis in the above formula be regarded as a single independent variable, the formula for s can be treated as a simple product and quotient of four variables, namely, the rise of temperature of the calorimeter and contents, the fall of temperature of the substance, the weight of the substance, and the weight of the water plus the water equivalent of the cal- orimeter. Suppose it is desired to determine s to 0.5 per cent. What will be the allowable deviations in these four compoments? Solving for "Equal Effects" we have at once 8(w + k) _ S(to fr) _ Sw _ S(t s < 2 ) _ 1 ds _ 0.005 Wo + k ' ' t 2 ti iv ~' t s tt ~ ^/4~ -s 2 All four factors must therefore be measured to 0.25 per cent. With the apparatus provided the following approximate values- may be assumed for illustration. Suppose w 300 gnis. then dw = 0.75 gm. Wo + k = 500 gms. " 8(w + A;) = 1 .2 gms. t* h = 20 1 5 = 5 5(^2 *i) = 0.013. f * 2 =100 20 = 80 " S(t s ~ -t z ) = 0.20. It is evident from these results that the greatest difficulty in attaining the desired degree of precision is in the determination of the rise of temperature in the calorimeter. For a rise of five degrees, the allowable deviation after all thermometric and radiation corrections have been applied, must not be greater than 0.013 and this cannot be attained without considerable skill and care. 60 NOTES ON PHYSICAL LABORATORY EXPERIMENTS To measure the fall in temperature of the substance to 0.2 through a range of 80 necessitates a careful determination of the correction of the thermometer used, at 100. On the other hand the weight of the substance w can be deter- mined with ease to ten times the required precision with an ordi- nary balance. If therefore w be weighed to 0.07 gram or even 0.1 gram, the error in it may be assumed negligible, and hence the allowable deviations in the temperature measurements may be a little greater without increasing the deviation of the final result to more than 0.5 per cent. The deviation in w + k may also be made negligible as the following consideration will show. Suppose, as in the experiment, that the specific heat of all the material composing the calorimeter, stirrer, etc. is 0.095 and that its total weight is about 100 grams. Then k = 9.5. If the value 0.095 is reliable to a per cent, i.e., about one unit in the third decimal place, and if the calorimeter stirrer, etc., be weighed to one per cent or better 0.5 per cent, i.e., the nearest half gram, the value of k = 9.5 will be reliable to one unit in the tenths place. Hence if the water be weighed to the nearest 0.1 gram or 0.2 gram as may easily be done, the resulting deviation in w + k = 500 grams will not be more than 1 or 2 parts in 5000 and hence negligible, and this result can be attained without materially in- creasing the difficulty of the experimental work. Under these conditions the function can be treated as one of two variables and we obtain as allowable deviations in the temperature differences, l(U ij) a(fr *i) 0.005 = u.ouoo, is - 2 fg - t\ from which if t s t 2 = 80 S(t s t 2 ) = 0.29 and tz ti = 5 (fc *i) = 0.16. If the allowable deviation in the difference of two quantities '2 *i i g &> then the allowable deviation in each of the component quantities is . . Hence the allowable deviation in each reading , . . , 0.016 V^ 0.29 and 2 2 of the calorimeter thermometer will be ""~" = 0.01 1C. and in the readings t s and * 2 > ~~7= := - LATENT HEAT OF VAPORIZATION Problem. From a consideration of your data on the sub- stance investigated and the above precision discussion, calcu- late how precise the following quantities should be deter- mined, in order to ensure an accuracy of one per cent in the value of the specific heat: a, the rise of temperature in the calorimeter ; b, the fall of temperature of the substance ; c, the weight of the substance; d, the weight of water in the calorimeter. LATENT HEAT OF VAPORIZATION CONDENSATION METHOD Object. The object of this experiment is to determine the latent heat of vaporization of a liquid by the Condensation Method. The experiment affords an excellent example of a typical calorimetric measurement. Discussion. When a substance passes at constant tempera- ture and pressure from one physical state to another, e.g., from solid to liquid, or liquid to vapor, etc., a certain quantity of heat is absorbed or evolved, the amount of which correspond- ing to the transformation of one gram of the substance in ques- tion is known as the latent heat of the reaction. Thus if the reaction considered is the change of one gram of water from the liquid to the vapor state, the heat required to affect this change under the above conditions is called the latent heat of vaporization. It is the negative of the latent heat of con- densation, i.e., the heat evolved when one gram of saturated vapor condenses to one gram of liquid at constant pressure and temperature. The latent heat of any reaction consists in general of two parts, one corresponding to the energy involved in the molecular changes accompanying a change of physical state, and the other corresponding to the external work which is done by, or on, the system as a result of its change of volume against a constant pressure. The former may be spoken of as the change in the internal energy of the substance and will be denoted by e; the latter, the external work, is given by the 62 NOTES ON PHYSICAL LABORATORY EXPERIMENTS expression p (r 2 - vj where v 2 and v lf are the specific volumes of the substance in the initial and final states, respectively. The latent heat may therefore be written .r e + p(v 2 -v 1 ). Of the terms in this fundamental expression, only r can be measured directly; e itself is not capable of direct measure- ment; p (r a TI) can be at once computed when the pressure p and the specific volumes r 2 and Vi are known. Thus in the case of the vaporization of water at 100 C., and under atmospheric pressure, 760 mm., i\ = 1.043 r 2 = 1661 cc., and the value of the external work in calories is 40.2. The total number of calories r required to vaporize one gram of water under these conditions is 536.5, hence of the total energy required to vapor- ize the water, 92.5 per cent is expended in doing internal work and 7.5 per cent in overcoming the atmospheric pressure during the expansion. The latent heat of any reaction diminishes with rising tem- perature, being zero at the critical temperature for the particu- lar change of state considered. From Regnault's data, Clausius has deduced the following empirical formula for the latent heat of vaporization of water between the temperatures C. and 200 C., r = 607 0.708*. If the latent heat of vaporization of a substance is multi- plied by its molecular weight m, the resulting product mr = A is called the molecular heat of vaporization. Important stochio- metrical relations have been found to hold for the values of this quantity for different liquids. Thus it is found that = const. for a large class of analogous liquids, where T is the absolute boiling temperature. This relation is known as Trouton's law. The numerical value of the constant depends on whether the molecular weight of the liquid is equal to or greater or less than that of its vapor. The most important methods for the determination of the latent heat of liquids may be classified as follows: First. The Condensation Method in which the quantity of LATENT HEAT OF VAPORIZATION 63 heat given out by the condensation of a measured weight of vapor is determined. Second. The Vaporization Method in which the amount of heat absorbed by the evaporation of a measured weight of liquid is determined. Third. The Electrical Method in which the quantity of liquid vaporized at its boiling point by heat developed elec- trically in a heating coil placed within the liquid is measured. Apparatus. The apparatus used in this experiment is shown in figure 13. The water is boiled in the vessel A which is closed by a cover setting into a water seal B, thus preventing Fig. 13. the escape of the steam at the top. The steam passes through a small tube D sealed tangentially into the cylinder E, a section of which is shown in figure 14. It circulates with considerable velocity around the inside of E, leaving it by means of the central tube from which it passes on to the calorimeter. The object of this device is to deprive the steam of any moisture which it may carry mechanically. This is deposited on the inner wall of the little cylinder and drops back into the water through small holes in the bottom. Unless the sterm is "dry" an accurate deter- minatirn of its latent heat is impossible. . 14. 64 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The calorimeter is of the closed type, of nickel-plated cop- per, and has a capacity of from one and one-half to two liters. It is shown in position for a run, resting on corks inside a water jacket J, which protects it from outside temperature changes. In the centre of the calorimeter is placed the con- densing coil C which should be nearly completely immersed in water. In the base of the condenser is a bearing for the stirrer which is mechanically driven by means of a small electric motor so pivoted at X that it can be swung back out of the way, or connected with the stirrer, as desired. The condenser is connected with the boiler by means of large heavy rubber tubing R and a brass elbow F lagged with felt to prevent condensation of the steam. The brass tube passing through the stoppers projects well up into F so as to form a trap for collecting any water which may become con- densed before the steam reaches the condenser. The steam should enter the condenser well below the surface of the water, otherwise the water around the neck of the coil is likely to be- come unduly heated, thus causing excessive evaporation and consequent error in the temperature of the water in the calo- rimeter. P is a clamp for closing the rubber connecting tube, and S is a screen for protecting the calorimeter from the heat of the burner and boiler. Procedure. Preliminary. ' See that all parts of the appara- tus, water jacket, calorimeter, coil, stirrer and cover have the same number. Rinse out the boiler and fill it with about two inches of clean tap water. Fill the water seal, place the cover on the apparatus and allow the water to boil some time so that the steam may warm up the connecting tubes R and F before the experiment proper. In the mean time pour out any water which may be in the condenser and weigh the condenser to centigrams. The exact weight of the coil when perfectly dry is given with the apparatus and the difference between this weight and the weight found is to be taken as so much addi- tional water in the calorimeter. Weigh the calorimeter, cover, and stirrer together, as they are all of the same material, to the LATENT HEAT OF VAPORIZATION DO nearest half gram. Next place the coil and stirrer in the calo- rimeter, fill the calorimeter to within a quarter of an inch of the top with clean tap water, put on the cover, and weigh all together to the nearest half gram. The weight of water can then be found by difference. Next take the temperature of the water jacket, which should be nearly that of the room in which it stands continually. In the morning it will often be found below this temperature owing to the fall in temperature during the night. In this case it should be warmed by flashing a burner on the outside of the jacket, stirring the water within in the mean time by blowing into it through a glass tube. In this experiment the rise of temperature is at a uniform rate during the operation and hence the Rumford Method of correcting for radiation is applicable. As the temperature is to be allowed to rise not over 10 or 12 C., the initial temperature of the water in the calorimeter should be adjusted to about 5 or 6 below the temperature of the jacket. Under no circumstances should the temperature of the calorimeter be so low that moisture precipitates upon it from the atmosphere. The outside of the calorimeter and inside of the jacket should always be thoroughly dry. When the tem- perature is adjusted put the apparatus together as in the figure. Before connecting 'the coil with the boiler, the cover should of course be removed from the latter and the clamp P closed so that ns. 66 NOTES ON PHYSICAL LABORATORY EXPERIMENTS Experiment Proper. The temperature readings are to be taken without interruption every half minute throughout the whole experiment. First. Take preliminary half-minute temperature readings of the calorimeter for six to eight minutes. Second. Open P, put on the cover of the boiler and note the instant when the temperature begins to rise suddenly. Continue reading the temperature of the calorimeter every half minute until the temperature has risen 10 or 12 C. Third. Take off the cover, close P and continue taking temperatures for six to eight minutes longer. Fourth. Remove the coil, dry the outside very carefully, and weigh as soon as possible to centigrams. Fifth. Record the reading of the barometer and its attached thermometer. Computation. Make a plot of the time and temperature ob- servations and determine the corrected final temperature t% of the calorimeter by special method I or II (pp. 52-54); find from proper tables, the temperature t s of the steam under the reduced barometric pressure at the time of the experiment. Let r = latent heat; w c = weight of the condenser dry; w = weight of water condensed in the coil; w = weight of water in calorimeter; MI + W 2 + w z = weight of calorimeter, cover and stirrer; j = corrected initial temperature of calorimeter; / 2 = corrected final temperature of calorimeter; t s = corrected temperature of steam; s c , !, s a , s 3 = specific heat of the condenser and parts of calo- rimeter, respectively. ' These may all be assumed equal to 0.095. The heat given out by the steam in condensing to water at t s plus the heat given out by this water in cooling to t% is equal to the quantity of heat corresponding to the rise of temperature of the calorimeter and its contents, that is rw + w (t, y = (w + k) (^ y, from which r = w MECHANICAL EQUIVALENT OF HEAT I 67 where k is the water equivalent of the calorimeter, cover, stirrer, and condenser, i.e., k = w c s c + uy?i + wfa + W 3 s 3 = 0.095 (w c + w 1 +w 2 + wj. Problem. From a consideration of the magnitude of the quantities measured in this experiment, calculate approxi- mately how precise the following quantities should be deter- mined in order to attain a precision of one-half of one per cent in the final value of the latent heat: a. Rise of temperature in calorimeter; b. Fall of temperature of condensed steam; c. Weight of condensed water; d. Value of total water equivalent (w + fc) of the calorim- eter and contents. MECHANICAL EQUIVALENT OF HEAT I Object. The object of this experiment is to determine the value of the mechanical equivalent of heat by the electrical method. The experiment furnishes further practice in calo- rimetry and in the measurement of quantities of energy. A study of the electrical apparatus employed is also very instruc- tive as illustrating the transformation of high potential direct currents to direct currents of low potential. Discussion. The mechanical equivalent of heat is the value of one calorie expressed in ergs, that is, the factor for reducing heat energy expressed in calories to mechanical energy ex- pressed in ergs. Until recently all exact determinations of this quantity, Joule's, Rowland's, and others, consisted essentially in measuring the quantity of mechanical energy transformed by some device directly into heat energy, the amount of which was measured calorimetrically. If a ergs are found to pro- duce b calories, by the principle of the conservation of energy, these two quantities of energy must be equal, i.e., a ergs=.& calories, and the factor J = - is therefore the desired factor for reducing calories to ergs. 68 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The same result may be equally well obtained if some other form of energy, e.g., electrical energy be transformed into heat, provided, first, that the relation of the units in which it is meas- ured to the erg is exactly known, and second, that electrical energy can be measured with the same degree of accuracy as mechanical energy. With the refined methods and instruments of electrical measurement at our disposal, this is now possible, as recent determinations of the mechanical equivalent by wholly electrical means have shown. 1 The determination of this fundamental physical constant with a high degree of accuracy requires elaborate apparatus and very careful manipulation. An accuracy of half of one per cent may be obtained, however, without much difficulty. The method consists in measuring the electrical energy ex- pended in heating a coil of wire placed in a calorimeter, on the one hand, and the heat energy thereby resulting, on the other. As the heating effect of a current is given by the expression Q = lEt or Q = PRt the electrical input may be obtained by measurements either of current, voltage, and time, or cur- rent, resistance, and time. The former method is the more convenient and direct, as by it we measure the two factors which primarily constitute electrical energy, namely, potential and quantity of electricity (current X time). Moreover both of the quantities / and E can be determined with an accuracy of 0.1 or 0.2 per cent, by direct-reading instruments. The measurement of the heat energy is made in the usual way, all precautions necessary to accurate calorimetric measurements being observed. A precision of two or three tenths of a per cent can be obtained without serious difficulty. Apparatus. The apparatus consists of' a closed calorimeter resting on cork supports inside a water jacket. The heating coil of flattened manganine wire fits concentrically inside the calorimeter. Manganine is employed on account of its very low temperature coefficient, and the wire is flattened so as to : give a greater radiating surface. Inside the coil and supported by the frame is the stirrer, carrying two sets of vanes, which, i Griffith, "Determination of Mech. Equiv. of Heat," Phil. Trans., 184, p. 361, .1893. MECHANICAL EQUIVALENT OF HEAT I 69 when rapidly rotated by a small hot-air engine, keeps the water in violent agitation. The brass terminals of the coil project through insulated holes in the cover, and can, after the calo- rimeter, coil and cover are in place, be easily connected by flexible leads to the source of current. The current is furnished by a motor-generator running on the 220 volt circuit and delivering energy at 12 volts. A low voltage is desirable in this experiment to avoid electrolysis. By means of a heavy fly wheel and the device of "floating" a set of batteries across the terminals of the heating coil, fluctu- ations arising from variations in the impressed voltage can be almost wholly eliminated. The generator is to be started by an instructor who will explain further details. A storage battery of large capacity is also very well suited for furnishing electrical energy for this experiment. The current is measured by a Weston ammeter which is con- nected in series with the heating coil. The potential at the terminals of the heating coil is measured by a Weston volt- meter connected by potential leads to these points. The cir- cuit is made and broken by a knife switch. Procedure. Two students will be assigned together to this experiment. Data should be recorded on blanks made out before the exercise, similar to those in the sample notebook. Preliminary. Weigh the calorimeter, cover, and coil dry. The weights and specific heats of the individual parts of the heating coil are given with the apparatus. Place the coil in the calorimeter and fill the latter with cold tap water so that the coil and frame are completely immersed, and weigh. The tem- perature of the water should be at least three or four degrees below that of the water in the jacket. Set up the apparatus for a run. Start the hot air engine and stirrer. After the latter has been in action some minutes note the temperature of the calorimeter, and also that of the inside of the outer water jacket; the latter should be at about room temperature, and several degrees above that of the water in the calorimeter. Since in this experiment the rate at which heat is put into the calorimeter is practically uniform from 70 NOTES ON PHYSICAL LABORATORY EXPERIMENTS start to finish, the Rumford method of eliminating the radi- ation correction may be advantageously employed. The rise of temperature in the calorimeter should be about five degrees; the initial temperature of the calorimeter should therefore be brought up to within 2.5 of that of the surroundings. This can be done exactly by closing the circuit for a few minutes and allowing the current to heat up the water in the calorim- eter by the proper amount. The circuit should never under any circumstances be closed unless the heating coil is wholly immersed in water. The apparatus and connections should be inspected by an instructor before the circuit is closed. Experiment proper. Having adjusted the initial tempera- ture of the water in the calorimeter, all is ready for the run. One student A, is to open and close the circuit and read the voltmeter and ammeter; the other B, is to read the thermometer. Each should prepare blanks beforehand for recording his ob- servations. Temperatures are to be taken every half minute, and voltmeter and ammeter readings alternately every fifteen seconds. A preliminary series of temperature readings are to be taken for five minutes before closing the circuit; then at a noted instant, preferably on the minute, the circuit is closed, and voltmeter and ammeter read instantly. When the tem- perature has risen nearly five degrees, B, reading temperatures, should notify A, who, at a noted instant, opens the switch. The switch should be opened and closed as nearly at the noted times as possible, so as to reduce the error in the time measurement to a minimum. The temperature of the calorimeter should be continuously observed five minutes longer to provide all neces- sary data for correcting for radiation and mechanical heating due to stirring, if these be not wholly eliminated by the above- described method of procedure. This completes one set of data. The water in the calorimeter should then be cooled to a tem- perature below that of its surroundings and a duplicate run made in exactly the same manner, A and B changing places. Computation. The calorimetric data are to be plotted and the corrected rise of temperature determined as described under special case, I or II, pp. 52-54. The computation of the elec- MECHANICAL EQUIVALENT OF HE./VT I 71 trical energy is to be made as follows: Since all ammeter and voltmeter readings are taken at equal time intervals, the mean voltage and current multiplied by the total time may be taken without error for the sum of the products of each pair of readings multiplied by the corresponding time interval. The mean value of the current and voltage must be corrected for instrumental errors. The calibration corrections of the in- struments used will be found with the instruments. The "zero error" should be observed by the student. Without careful calibration, the instruments cannot be assumed correct to 0.1-0.2 per cent. The product, current (in amperes) X potential (in volts) X time (in seconds) gives the total electrical energy expended in heating the calorimeter, expressed in joules. Equating this quantity to the number of calories actually measured, the value of one calorie expressed in the practical unit of electrical energy, the joule is readily obtained. To reduce this value to the ab- solute unit of energy, the erg, we must know the value of a joule in ergs. The system of electrical units is so defined that one joule = 10 7 ergs. Each student is to compute one run independently, but the final results of both are to be handed in for comparison. Problems. How many joules are necessary to vaporize 100 grams of water at its boiling point under standard condi- tions of pressure? If this energy is supplied at the rate of 100 watts, what time will be necessary? If the resistance of the coil is 10 ohms, what current and voltage will be necessary? With a 110- volt pircuit what must / and R be? 2. What must be the percentage precision of /, E, and t in order that the resultant deviation in Q is not greater than 0.5 per cent? 3. What are the allowable deviations in amperes, volts, and seconds corresponding to the precision prescribed in problem 2 if the value of /, E, and t are the mean values found in the ex- periment? Do you think this degree of precision was attained? 72 NOTES ON PHYSICAL LABORATORY EXPERIMENTS MECHANICAL EQUIVALENT OF HEAT II CONTINUOUS CALORIMETER Object. The object of this experiment is to give prac- tice in the use of a continuous calorimeter for measuring heat energy. The method is illustrated by a determina- tion of the mechanical equivalent of heat by the electrical method. Discussion. The principle of a continuous calorimeter is as follows: Heat is generated at a uniform rate within a calo- rimeter which is so constructed that the heat can escape only by conduction and radiation through a stream of water which circulates through the apparatus. The temperature of the in- coming water must be below the temperature of the room (surroundings); its rate of circulation through the calorim- eter is so regulated that its temperature when it leaves the apparatus has been raised just to the temperature of the room. Under these circumstances the outflowing water con- ducts away, at a constant rate, the heat generated within the calorimeter, and the amount of heat generated in a given time will be measured by the quantity of water flowing in that time, multiplied by the rise of temperature which the water has experienced in passing through the apparatus. A determina- tion of the difference in temperature of the incoming and out- going water when a state of equilibrium has been established in the calorimeter, and of the quantity of water flowing through in a given time, furnishes therefore all 'data necessary for computing the rate of heat development within the calorim- eter. A little consideration will show that, in order that a state of thermal equilibrium may be established within the apparatus the following conditions must be fulfilled: (a) The heat must be generated uniformly. (6) The water must flow uniformly, i.e., under a constant pressure. 1 UNIY-.-.SITV V r \S MECHANICAL EQUIVALENT G^^Ji^^^^ 73 (c) The temperature of the incoming water must be con- stant. (d) The temperature of the surroundings must be constant. Under these conditions it is to be particularly noted that the usual correction for radiation, so troublesome in most calori- metric experiments, may be entirely eliminated, for, if the out- going water is caused to circulate within the outside wall of the calorimeter, and its temperature is maintained the same as the tem- perature of the surrounding air, there will be no exchange of heat by the apparatus either by radiation or con- duction to or from the surroundings, no matter what may be the duration of the experiment. The apparatus described below is designed to meet the above require- ments, and to give the calorimetric results reliable to at least 0.5 per cent. Apparatus. The general arrange- ment of the apparatus is shown in Fig. 15. The water is piped directly from the street mains, in order to in- sure a constant temperature below that of the laboratory, into an over- flow tank A, placed about ten feet above the apparatus, which furnishes a supply at a constant pressure. The water from the tank flows down into the calorimeter at B, circulating up and down around an enclosed heating coil, as shown in Fig. 16, and finally leaves it at C. D is a three-way cock, by means of which the water can be run off into the waste pipe E, or collected through F. The temperature of the incoming water is taken by the thermometer inserted at B, and of the outgoing water at C. Fig. 15. 74 NOTES ON PHYSICAL LABORATORY EXPERIMENTS The details of the calorimeter are shown in Fig. 16. It consists of a small inner brass tube around which, but insu- lated from it, are wound a number of turns of fine ger- man-silver wire. In order to insulate the wire and also to facilitate the con- duction of the heat gen- erated in it to the water, the coil is completely im- mersed in oil. The incoming water passes down through the heating coil and then circu- lates up and down through the calorimeter as shown in the figure. A pinch-cock regulates the flow at P. A small reservoir R, con- nected to the oil-jacket, serves to receive the over- flow due to the expansion of the oil when heated by the current in the coil. The calorimeter is placed inside a metal jacket to protect it from draughts. Both calorimeter and jacket are nickel-plated and highly polished to diminish the radiation. A vessel for collecting the water and suitable scales for weighing it are provided. The electrical measuring instruments required consist of a portable Weston ammeter and volt-meter, the former being connected in series with the heating coil, and the latter across its terminals. The coil is connected directly to the 110-volt mains. The instruments are calibrated and their corrections will be found on them. Fig. 16. MECHANICAL EQUIVALENT OF HEAT II 75 Procedure. This experiment is to be performed by two stu- dents working together. Data should be recorded similar to those in the sample note-book. All pipe and electrical connec- tions should be explained by an instructor before the experi- ment is begun. Preliminary. Allow the water to flow through the apparatus with the pinch-cock P, which regulates the outflow of the water from the calorimeter, wide open so that a full stream runs through the calorimeter into the waste pipe E. Close the cir- cuit containing the heating coil. When the temperature of the inflowing water has become constant to 0.2 for at least two minutes, begin regulating the outflow by the pinch-cock P so that its temperature approaches that of the room. While waiting for the outflowing water to come to a constant temperature, weigh the vessel for collecting the water and arrange the blanks for recording the observations. When the outflowing water has come to a constant temper- ature, note whether it is above or below that of the surroundings, i.e., the temperature of the air just inside the calorimeter jacket. If above, open the pinch-cock slightly to allow the water to flow more rapidly, and wait until the temperature again becomes con- stant. If below, close the pinch-cock slightly, and wait as be- fore. A fraction of a revolution of the pinch-cock screw will be found to produce a considerable variation in the ultimate temperature of the outgoing water. When the stationary con- dition of temperature is reached, the temperature of the out- going water should not vary more than 0.l in three minutes. Continue this operation (being sure to wait long enough after each adjustment for equilibrium to be established) until the temperature of the outgoing water is within 0.2 of that of the surroundings. When this condition is reached, but not before, begin the experiment proper. Experiment proper. One student will give the signals and note the times of starting and stopping the run, and will record readings alternately of the voltmeter and ammeter every fif- teen seconds for ten minutes. The other student will begin to collect and stop collecting the water at the signals- given, weigh 76 NOTES ON PHYSICAL LABORATORY EXPERIMENTS the water, and record the temperatures of the ingoing and out- coming water alternately at intervals of fifteen seconds during the run. The temperature of the surroundings should also be recorded at the beginning, middle, and end of the run. A short time, half a minute or so, before beginning the run, turn the three-way cock so that the water will flow out through F into any convenient vessel. Then at the signal for starting the run, begin to collect the water for weighing by quickly placing an appropriate vessel of four litres or more capacity under F. This procedure for collecting the water has been found to introduce less initial error than turning the three-way cock from E to F at the starting signal. At once begin to read the temperatures of the incoming and outgoing water. At the signal for concluding the run (duration about ten minutes), stop collecting the water by pinching the end of the rubber tube with the fingers, and at once turn the three-way cock so that the water will again flow into the waste pipe E. Weigh the quan- tity of water collected. This completes one set of data. The run should be repeated, the two observers changing places. Computation. The electrical input is to be computed from the mean ammeter and voltmeter readings corrected for zero and calibration errors, and the time. The corresponding value of the heat energy evolved is to be computed from the mean differ- ence of temperature of the incoming and outgoing water and its weight. If the temperature readings are nearly constant, as they should be, the difference' of the mean temperature of the incoming and outgoing water may be used in the compu- tation. The thermometers used must be very carefully compared with each other. The corrections are given. Each student is to compute one run independently, but the final results of both are to be handed in for comparison. The problems on page 71 should also be included unless previously handed in. EXPANSION The determination of the coefficients of expansion of liquids, solids, or gases with any high degree of precision requires skill- ful manipulation and attention to numerous details and cor- rections, and not infrequently the use of least squares in the reduction of the data. Special apparatus including compara- tors, and Abbe's Dilatometer (Fizeau's apparatus), is provided for this work, which is offered to students who are qualified to undertake it. The work is not required however in the in- troductory laboratory course. APPENDIX The data in the following abbreviated tables are taken from Landolt and Bornstein's " Physikalisch-chemische Tabellen." B TABLE I. LINEAR COEFFICIENTS OF EXPANSION. Aluminium . 0.000023 Lead . . . . 0.000029 Brass 0.000019 Platinum . . ... 0.000009 Copper 0.000017 Platinum-ir id ium 0.000009 German Silver Glass ordinary 0.000018 0000085 Silver Tin 0.000019 000023 Gold 000015 Vulcanite 00008 Iron . 000012 Zinc . 000029 Wood with the grain 0.000003 to 0.000010 Wood across the grain 0.000033 to 0.000061 TABLE II MEAN CUBICAL COEFFICIENTS OF EXPANSION BETWEEN AND 100. Benzene 00138 Mercury 000181 Toluene 00121 Ether 000215 Turpentine 0.00105 Alcohol 00104 Chloroform 0.00140 000534 For water, V t = V (l + at + bt* + where a = 0.00006581. 6 = + 0.00000851. C = 0.000000068. v = volume at C. v t = volume at t C. APPENDIX TABLE III. MEAN COEFFICIENTS OF EXPANSION OF GASES BETWEEN A^D 100. Volume Constant. Pressure Constant. Air . . 0.003669 0.003671 Oxygen 0.003674 Hydrogen 0.003668 003661 Nitrogen 0.003668 Carbonic Oxide 0.003667 0.003669 Carbonic Acid 0.003706 0.003710 Nitrous Oxide 0.003676 0.003720 TABLE IV. MELTING POINTS (HOLBORN & DAY, 1901). Cadmium 321 7 1 (From 10 observations on two days.) Lead 3269dbO2 " " " " " " Zinc Antimony Aluminium Silver Silver Gold Copper 419.9 0.2 630.5 0.3 657.5 0.5 (In a graphite crucible, a lower value. 961.5 0.9 (Pure ; i.e., in a reducing atmosphere. 955 (In air; point ill denned.) 1064 1065 (In air ) Copper 1084. (Pure.) TABLE V. BOILING POINTS OF LIQUIDS AT 760 mm. PRESSURE. Water . ; 100 C. Benzene 80.0 Mercury 357 03 Glycerine 290 Sulphur 444 Alcohol 78 2 Naphthaline . . . . .. . Toluene 218.0 110 Turpentine Chloroform 159.0 61 2 80 APPENDIX TABLE VI. LATENT HEATS OF VAPORIZATION EXPRESSED IN O CALORIES. Temperature of Vaporization. Latent Heat. 350 62 00 Alcohol 78 206 4 Ether . . . . 34.9 89.96 Toluene ...... 110.8 83.55 Turpentine 159.3 74.04 Ammonia 7.8 294.2 Benzene . . 80.1 92.91 Water 100 536 2 (15 to 16) Clausius's formula for the variation of the latent heat of vaporization of water with the temperature is, r = 607 .7Q8t when t is the temperature of vaporization in degrees centigrade. TABLE VII. SPECIFIC HEATS OF VARIOUS LIQUIDS AND SOLIDS. Alcohol at 17 0.58 Glass between 15-100 . . 0.20 Aniline " " 0.49 Gold " . 0.032 Benzene " " 0.36 Iron "... 0.113 Mercury " " 0.034 Lead " "... 0.032 Toluene " " 0.40 Nickel " *' . 0.11 Turpentine at 17 . . . 0.43 Platinum " "... 0.033 Aluminium between 15-100 . 0.218 Quartz " "... 0.191 Brass " " 0.093 Silver " "... 0.057 Fluorspar " 0.208 Tin " "... 0.056 Copper " 0.093 Zinc M . . . 0.094 APPENDIX 81 TABLE VIII. TEMPERATURE, PRESSURE, AND SPECIFIC VOLUME OF SATURATED VAPOR.i Temperature in Degrees Centigrade. Pressure in mm. of Mercury. O rn ail %>a Temperature in Degrees Centigrade. Pressure in mm. of Mercury. Specific Volume in c.cm. Temperature in Degrees Centigrade. Pressure in mm. of Mercury. rt ||| > B 4.602 211500 38 49.308 21860 76 300.83 3965 l 4.941 197700 39 52.05 20770 77 313.59 3813 2 5.303 184600 40 54.91 19740 78 326.80 3668 3 5.689 172400 41 57.92 18760 79 340.48 3529 4 6.100 161200 42 61.06 17840 80 354.63 3397 5 6.536 150800 43 64.35 16980 81 369.27 3270 6 7.001 141200 44 67.80 16160 82 384.41 3149 7 7.494 132200 45 71.40 15390 83 400.08 3033 8 8.019 123900 46 75.16 14660 84 416.27 2922 9 8.576 116200 47 79.10 13970 85 433.01 2815 10 9.167 109000 48 83.21 13310 86 450.31 2714 11 9.795 102300 49 87.51 12690 87 468.18 2616 12 10.460 96090 50 91.98 12110 88 486.64 2523 13 11.164 90190 51 96.65 11560 89 505.71 2433 14 11.911 84760 52 101.54 11030 90 525.40 2347 15 12.702 79690 53 106.64 10530 91 545.72 2265 16 13.539 74970 54 111.95 10060 92 566.70 2186 17 14.423 70560 55 117.49 9610 93 588.34 2110 18 15.360 66440 56 123.25 9185 94 610.67 2038 19 16.349 62580 57 129.26 8782 95 633.70 1968 20 17.395 58980 58 135.51 8399 96 657.45 1901 21 18.498 55610 59 142.02 8036 97 681.93 1836 22 19.663 52460 60 148.80 7687 98 707.17 1774 23 20.892 49510 61 155.85 7362 99 733.19 1715 24 22.188 46740 62 163.18 7051 100 760.00 1661 25 ' 23.554 44150 63 170.80 6754 101 787.5 1609 26 24.994 41720 64 178.72 6470 102 815.8 1556 27 26.510 39450 65 186.95 6201 103 845.0 1505 28 28.107 37310 66 195.50 5947 104 875.1 1456 29 29.786 35300 67 204.38 5705 105 906.0 1409 30 31.553 33420 68 213.60 5472 106 937.9 1365 31 33.411 31650 69 223.17 5250 107 970.7 1320 32 35.364 29980 70 233.09 5040 108 1004.4 1278 33 37.416 28420 71 243.39 : 4839 109 1039.1 1248 34 39.571 26940 72 254.07 4648 110 1074.7 1209 35 41.833 25560 73 265.14 4465 111 1111.4 1162 36 44.207 24250 74 276.62 4291 112 1149.1 1126 37 46.697 23020 75 288.51 4124 113 1187.9 1091 1 These values are taken from Peabody's Steam-Tables. MECHANICAL EQUIVALENT OF HEAT. l kilogram-calorie (1 kilogram water raised 1 C. at 15 C.) = 427.3 kilogrammeters (at sea-level, latitude 45, g = 980.6 c. g. s.). 1 British thermal unit (l pound water raised 1 F. at 59 F.) = 778.8 foot pounds at sea- level, latitude 45. 1 gram-calorie (1 gram of water raised 1 C. at 15 C.) = 4.190 X 10 7 ergs. l Joule = 10 7 ergs. = 0.2387 gram-calorie. REC'D LD DEC 2 9 1961 fB 4 1933 24Mar'6lCK