TP RANP'S SCIENCE SERIES. ) 3- STOST3 ~' '" '&^^^l jvE-MAKIN MACHINES' THF TH1 ; I'lON OF TH ;: VART- .': ' : ' .M.- J^^l A i-lK . ' r.\: FROM THE -'F:NCH OF M. LEDOUX. tfKUff*- D.VA1- .^TOSTKAND, 23 MUHVvAY AND ^T WARREN STREET. 1879. uuivs,E;'srrlf ICE-M7OUNG- MACHINES: THE THEORY OF THE ACTION OF THE VARI- OUS FORMS OF COLD-PRODUCING OR SO-CALLED ICE MACHINES ( MACHINES A FROID). TRANSLATED FROM THE FRENCH OF M. LEDOUX, Ingenieur des Mines* REPRINTED FROM VAN NOSTRAND'S MAGAZINE. NEW YORK: D. VAN NOSTRAND, PUBLISHER^ 23 MURRAY AND 27 WARREN STREET. 1 8 79. PREFACE. THE theory of Ice-Making Machines has assumed a new importance, since it has been shown that they may be worked to an economical advantage in some sec- tions, even where natural ice is not diffi- cult to be obtained. But aside from any question of com- petition with natural ice in temperate climates, the subject is of great interest to those who find it desirable to produce and maintain a low temperature in places where the requisite quantity of ice would be too cumbersome, and where a refrig- erating machine and its driving power can be easily accommodated. Such an example is afforded by the hold of a ves- sel sailing in a warm climate. The conditions of effective working of the three classes of machines are clearly set forth in this little treatise. G. W. P. ICE-MAKING MACHINES. CHAPTER I. 1. IT has long been known that air is heated or cooled when compressed or dilated. The mechanical theory of heat defines the conditions under which this heating or cooling is effected, and shows that these effects are proportioned to the ex- ternal work performed by the air, with the restriction that in expanding the resist- ance overcome by the gas is always equal to the elastic force of the latter. If t and t' represent successive tempe- ratures of a unit weight of a permanent gas, which has been compressed or dila- ted under conditions above stated in producing an amount of work (either re- sistant or motive) equal to W, we shall have A being the reciprocal of the mechan- ical equivalent of heat =^-|^- and c being the specific heat of the gas at constant yolume. In a saturated vapor a part of the ther- mal equivalent of the external work is transformed into latent heat; the other part alone becomes sensible under the form of external heat. This is expressed in the fundamental equation in which c l is the specific heat of the liq- uid, x the proportion of vapor in the unit of weight of mixture of liquid and vapor, p the latent heat of the vapor and W the external work accomplished. We see from these equations that for the same quantity of heat transformed into work, the range of temperatures must be greater with a gas than with saturated vapors. 2. Whether we employ a permanent gas or a vapor, the apparatus designed for the refrigerating effects is based upon the following series of operations : Compress the gas or vapor by means of some external force, then relieve it of its heat so as to diminish its volume ; next, cause this compressed gas or vapor to expand so as to produce mechanical work and thus lower its temperature. The absorption of heat at this stage by the gas, in resuming its original condition, constitutes the refrigerating effect of the apparatus. When the cooling takes place at con- stant pressure, the cycle of operations can be represented by the diagram Fig. 1 in which the abscissas represent volumes, and the ordinates pressures. The gaseous body taken at the press- ure P and under the volume V is com- pressed to the tension P x and the volume Vj. It is then cooled under constant pressure so that the volume Vj becomes V/, then it is allowed to expand, the pressure P l becoming P and the volume changing from V/ toV 2 . Finally it is brought to the original volume V by transferring heat to it under constant pressure. The area V^jV/V,, represents 9 the work expended and the lineV V 2 the refrigerating effect obtained. An inspection of the figure shows that a refrigerating machine is a heat engine reversed. If instead of cooling the gas, to reduce it from the volume V x to V/, it be heat- ed so as to assume the volume V/' greater than 'V l an amount of work is obtained which is represented by the vertically shaded area V^'V/'V^ the heat expended is represented by the length V^/'. It should be noticed that in the case of a permanent gas, the changes from volume V to Y/ or V/' and from V 2 or V/ to V are accompanied by correspond- ing changes in temperature. In the case of a condensable vapor these changes are effected at a constant temperature, the addition or subtraction of heat taking effect in an evaporation of the liquid or a condensation of the vapor. / 3. From this similarity between heat motors and freezing machines it results that all the equations deduced from the 10 mechanical theory of heat to determine the performance of the first apply equally to the second. If Q, be the quantity of heat taken from or added to a given mass, of com- pressed gas or vapor, and Q the quan- tity of heat necessary to subtract from or add to the expanded mass in order to bring it to its initial state, T and T l the absolute temperatures correspond- ing to the volumes V and Y x and W the work, either active or resistant devel- oped by the machine. The fundamental principle of the mechanical theory of heat, if the gas returns exactly to its primitive condition, affords the equation, Q i _Q=AW If the cycle, of changes is the so-called cycle of Carnot; that is to say, if the lines V^, Y/V 2 , and V/'V/ are adiaba- tic curves; then we have Q = Q. Q.-Q T T, T,-T The quantity of work developed by a heat motor, under these circumstances, 11 is for each heat unit or calorie, whatever the intermediate agent, The efficiency depends upon the dif- ference between the extremes of temper- ature. The performance of a refrigerating machine depends upon the ratio between the calories eliminated and the work expended in cooling. It is expressed by Q W and we have Q_ AQ T W-Q,-Q- A T,-T; This result is independent of the na- ture of the body employed. Unlike the heat motors, the freezing machines possess the greatest efficiency when the range of temperatures is small, and when the final temperature is eleva- ted. y In a freezing machine employing a va- 12 por, T being the absolute minimum final temperature, this final temperature T 2 in a machine employing a permanent gas is different from the initial temperature T , and we have, We can write for the efficiency Q = A T 2 Comparing the efficiencies of the two machines it is evident that the perform- ance becomes less in proportion as we obtain lower final temperatures. Theoretically there is no .advantage in employing a gas rather than a vapor in order to produce cold even if the com- pression be made without addition or subtraction of heat. The choice of the intermediate body would be determined by practical consid- erations based on the physical character- istics of the body, such as the greater or less facility for manipulating it; the extreme pressures required for the best effects, etc. 13 Air offers the double advantage that it is everywhere obtainable, and that we can vary at will the higher pressures in- dependent of the temperature of the refrigerant. But it is cumbersome, and to produce a given useful effect the appa- ratus must be of large dimensions. Liquids on the other hand allow the use of smaller machines, but are obtained only at a greater or less cost. Furthermore the maximum pressure is determined beforehand by the temperature of the refrigerant, and depending on the nature of the volatile liquid; this press- ure is often very high. 4. The foregoing conclusions are based on the hypothesis that the com- pression and expansion follow the adia- batic lines V V 1 and V/V a , that is to say that the changes of volume and pressure follow the cycle of Carnot. This hypothesis is realized when the cooling is accomplished outside of the compression cylinder and after the gas has been raised to the pressure P : . If the cornpresai^EpfcSFSEfeeted accord- OF THE UNIVERSITY 14 ing to some cycle different from Car- not's, the efficiency, if it be a heat motor, would be diminished, but in a freezing machine it would be greater or less, de- pending upon the manner in which the successive operations were effected. Suppose for example that instead of cooling, the gaseous body outside the compression cylinder, it be done during compression within the cylinder in such a manner as to maintain a constant temperature. This hypothesis would be graphically represented in Fig. 1 by re- placing the adiabatic curve V Vj by the isothermic curve V V/. The work of resistance of the machine would then be represented by the curvilinear triangle VjjVjV/V,,. The quantity of negative heat produced represented by the line V V 2 remains the same. The efficiency of the freezing machine would be thus augmented as the resistant work of the motor would be less than the preceding case for the same quantity of negative heat produced. The cooling of vapors during com- 15 pression is not readily realized, since it is effected at a constant temperature and one which is lower than the refrigerant. It is realized though somewhat incom- pletely in the case of permanent gases since their temperature during compres- sion is above that of the refrigerant. 5. The efficiency is calculated in the following manner. We suppose the compression to be made at a constant temperature. Then \ by Marriotte's Law we have P^^P^. The work of resistance to compression would be V V PV 7 "RT / r -^oV^y" tt-Vy' and we shall have as in the preceding case. AW r = Q, R is a constant, uniform for the air at 29.27 inches and a unit of weight is sup- posed taken. The gas dilating from the temperature T to T 2 without gaining or losing heat, we shall have for the work of dilatation, 16 inclusive of the work at full pressure during introduction ; The performance is represented by and we have A Q - Q.-Q *c(T.-T.) We have also c E Jc is the ratio of specific heat at constant pressure to the specific heat at constant volume; this ratio is =1.41 and is the same for all permanent gases. It follows then Qm nn A A A rrrA / If the compression follows an adiabatic curve, we shall have for the efficiency 17 calling T x the absolute final temperature of the compression O T T A *v A o 2 Q-Q~ T,-T -(T -T 2 ) - It is easy ft to show that k I Ztfr-i is greater than k O P O and consequently that the efficiency in the first case is less than in the second. The employment of air presents a cer- tain theoretical advantage over volatile liquids, inasmuch as it admits of cooling to a certain extent during compression. We will now examine in succession some of the recently invented freezing machines (machines a froid). The Air Machine of M. Giffard; the Sulphurous Acid Machine of M. Pictet, and the Am- monia Machine of M. Carre. 18 CHAPTER II. GIFFARD'S AIR MACHINE. 7. This machine consists of a single- acting cylinder A, the piston of which is furnished with two valves opening from without inward. This cylinder is sur- rounded with a jacket leaving a space within which circulates a current of cold water. There is a second cylinder, B, also single-acting, and having a solid piston, and with a diameter a little smaller than the first. At the bottom of this cylinder are two openings closed by valves, open- ing, one outward and the other inward, and operated by levers which are worked by cams on the driving shaft. The pistons are driven by crank con- nections with the main shaft. The condenser B is a surface condenser and receives a current of cold water from the envelope of the compressor cylinder A. A Keservoir of wrought iron, B', is connected with the condenser by a tube and communicates also with the bottom of the expansion cylinder B. 19 20 8. The air taken in at ordinary press- ure is compressed in the cylinder A till it has the density of that in the reservoir ; it is then allowed to flow into the con- denser B and the reservoir B'. During this passage it loses a great part of the sensible heat which it attains during compression, and is brought nearly to the temperature of the surrounding air. During this time the valve s of the cylinder B opens and permits a certain amount of air equal in weight, to that which is expelled from A, to pass from the reservoir into the cylinder producing a certain amount of work. Then the valve s closes, the air in the cylinder B expands producing again work which may be deducted from the work of compression and the temperature is lowered. When the piston B reaches the upper limit of its stroke, the valve s' opens and the cooled air as the piston descends escapes by the tube T. The cooling experienced by the air, during compression, by contact with the cooled sides of the cylinder is scarcely sensible. 21 The machine therefore acts under con- ditions set forth in 2 and we know that its useful effect cannot exceed the value T T Apir-^V or A,, ' m VJ - **m m i -*-o A i "* By means of the adjustable cams we can regulate at will the action of the valves s and s'. If we shorten the time of admission into the cylinder B, the pressure will increase in the reservoir; for the amount flowing into B should be equal to that forced into the reservoir from A. The temperature of the air ex- pelled will then be less. If, on the con- trary, we increase the time of admission the reservoir pressure will diminish, and the temperature of outflowing air will be increased. The apparatus presents then this im- portant peculiarity that we can vary the useful effect of the machine at will, through wide limits. As the air leaves B, at the pressure of the atmosphere, the minimum limit of pressure is established, below which the 22 expansion cannot be pushed, and which is controlled by the relative dimensions of the two cylinders. We will proceed to calculate the cool- ing effect produced by this machine and the corresponding work required. We shall neglect at first the effect of waste spaces in the machine, and of watery vapor in the air. 9. JLet P , t and T be the pressure and temperature (counted from absolute zero) of the air. V the volume described by the piston A. V x the volume of air when at pressure P r Vj is then the volume described by the piston during the out- flow. m= weight of air whose volume passes from Y to Vj. P l9 ^ and Tj the pressure and temperature of compressed air delivered from A. Y ' t ' and T ' the volume and 23 temperature after passing into the condenser. V 2 the total volume described by piston B. P 2 , Z 2 and T 2 the pressure and temperature of the air at the end of the course of this piston. During compression the cooling by simple contact with the sides of the cylin- der is insignificant. We shall neglect this and also assume that no heat is receiv- ed from the sides of the cylinder B. FIKST PEKIOD I COMPRESSION. .- 10. When air is compressed without losing or gaining heat, the pressure and temperature at each instant bear the re- lation to each other expressed by the equation P o V o * = p^t (1) in which k is the ratio of specific heat of constant pressure to the specific heat of constant volume. 0.23751 ~ 24 Gay Lussac's law affords, P V =BmT (2) and P 1 V 1 =EmT 1 (3) From equations 1 2 and 3 we deduce k 1 (6) The work of the resistance to compression and outflow is W ' - ^i( p 1 V i- p o V o)- (6) We have elsewhere k kc c being the specific heat of air of con- stant volume. Equation (6) then becomes W, =(T,-T.). (7) SECOND PEEIOD : COOLING. The air is cooled in the condenser under constant pressure. \ The volume 25 changes from V t to V/, and the temper- ature from t. to t'. T ' we have; V/=V-^- (8) and the quantity of heat imparted to the water of the condenser is ; Q^m&KT.-T/) (9) If T^T.thenB^AWr THIRD PERIOD; EXPANSION. The volume V/ of air enters the cylin- der B yielding an amount of work equal to PjV/. It expands from V/ to V 2 with- out gain or loss of heat. We have then: (11) (12) k 1 whence T^T/"^' (13) The work performed by the air is ' W m =( Tl '-T 2 ) (15) 26 The resistances to be overcome by exter- nal force amount to If the machine works properly, the final pressure P 2 should be equal to the at- mospheric pressure. The equations (10) (12) and (13) give V V __L o V ' ~~ V v T ' V * __ ILL V - T, T T and - f=* (18) *-! A l Equation (17) expresses the ratio which should exist between the volumes of the two cylinders, in order that the air be finally expelled at atmospheric pressure, after having been compressed by a force P,. The negative heat (cooling), produced by the apparatus, is the quantity of heat necessary to restore the air from the temperature Z 2 to the temperature t o9 under constant pressure. 27 Q=*c-(T -T 2 ) OT m *vWl_TA I" (19) 11. Since a given weight of air is re stored, at the end of the operation, to the same temperature and pressure it had at the beginning it follows, that it has been through a perfect cycle and we have from the mechanical theory of heat; The theoretical performance of the machine is, calling it ', Q = T -T 2 " " m m/ T,-T, - and as we have from equation (18) m rrv m m/ rp rp rr\ rp we get finally u=-A. - - - =A ^2 , (20) a result already found in 3 by suppos- 28 ing T/=T . If T X >T the useful effect is diminished. The efficiency of the machine will be all the greater as T a approaches in value to T ; that is to say as it is urged at a lower pressure into the reservoir. But as we lower the pressure of working, the quantity of negative heat produced dim- inishes also and becomes nothing when T/=T,. The necessary driving power W r W m which we proceed to calculate, should be augmented by the passive resistances. If we consider the refrigerating ma- chine as composed of two distinct ma- chines driven by the same shaft, we are led to consider that the work of the pass- ive resistances is proportional not to the final work W r W m but rather to the sum of the work developed in the two cylinders W r + W m . Considering the simplicity of the machine, the small amount of friction, and the absence of a stuffing box, we can admit that the work of the passive resistances should not ex- ceed eight per cent of the above total work. 29 The resistance of the machine is then The following table gives the amount of refrigeration obtained, and the work expended, by passing a cubic meter of dry air through the machine; the press- ures in the reservoir varying from 1 to 4 atmospheres. The temperature of the external air is taken at 15 ; the temper- ature of the air leaving the condenser at 18; temperature of the water about 13 V =l, T = 288 and w = l*.266. 12. An examination of the table shows the enormous influence that the passive resistances exert upon the efficiency of air machines. It is one of the conse- quences of the inherent cumbrousness which follows from the use of this body in a thermic machine. The useful effect produced is not in- creased in proportion to the increase of pressure. It is of no advantage to em- ploy pressures higher than about 4J at- mospheres. Aside from the diminution of efficiency of the air at high pressures, a loss is occasioned by heat developed in 30 ped. dev ori gat No. jnoq jad jaAiod asjoq jaj jnoq jad 19AiOd OSJOq 19 J i oo S S 8 T 1O O^ -H O CQ rH -i I rH il 00 O OOO O 'i O5 GO GO O Oi c-i o t> io i> to co GO tO ^ CO CO i> CO r-HGOOt^OlO^t 1 "^ 1 cSr-i-rHOOOOO OC:OOOOOO 'papuadxa 10^ CO^ rH^ CO^ 05 O^ O J> GO O5 TH O5 O O5 O "^ O5 -rfi J> O O5 TH 05 CO 1O* O GO O5 CO CO iO O H 1O to i> -> GO 5 i I 1O 1O CO J> 3 1O 10 O J> > rH O5 CO ^ 1O O T IO GO i i 1O tO C ^ CO 10 10 J paure^qo uorinuiraiQ; jive jo 9in:p3.i9din9j, rH TH GQ 3Q 04 Q^COrHOlOGOlOO ^O5 1O CO i> GO O5 O JH^H 10 05 C5 O GO 10 POiH CO ^ O t> i> GO -= 1 1 1 1 1 1 noissaidraoo iQiye JIB jo ofio i> o O5 -^H to *> T3 rHrHrH rHr-l \ (24) (P.-.pJV^BmT,, (25) ^V^BXT,. (26) The work of the resistance to compress- ionis 34 (27) or c' is the specific heat under constant volume of the superheated vapor c'= 0,3407. After cooling the volume becomes V'^V, ^ (28) *1 and we have ^V^RXTV From equations 21 and 22 we can de- duce the pressure in the reservoir. We can determine by examining a table of tensions of saturated steam whether the pressure p l is greater or less than the pressure which corresponds to the temperature T/. If it be less the air will not be saturated with vapor when leaving the condenser, and the heat ab- sorbed by the latter will be : If the pressure p l is greater than the 35 pressure />/, corresponding to the tem- perature T/ for saturated steam, there will be a condensation of some of the vapor in the condenser ; the amount con- densed will be /I.CL-O and the pressure of the vapor entering into the cylinder B will be p^, that of the air being P l p 1 f . We shall have also : aj / = Ai = i ; PO Pi P. P i We see that the quantity of vapor not .condensed by the cooling, and passing into the expansion cylinder, will continu- ally diminish in proportion as the work- ing pressure is raised. The influence of the humidity in the air will therefore be less as the pressure is made greater. The weight of the mixture of air and vapor, which is m -f /^ if there is no con- densation in the cooler or m + jt^x/ if there is a condensation, is carried into the cylinder B where it encounters the surfaces cooled during the preceding 36 stroke. We can neglect the influence of these cold surfaces upon the air alone, but not upon the mixture of air and vapor. The latter is converted into frost which releases a certain amount of heat to be imparted to the metal, and which during the expansion is restored to the air. Suppose at first that there is no con- densation in the cooler, there is conveyed to the cylinder a weight /^ of saturated, or nearly saturated, vapor at the tem- perature Tj'. We may assume, consider- ing the very low temperature of the sur- faces, that all the vapor is condensed here ; it will disengage a quantity of heat C, which is approximately equal to /^(r/4-79). r/ being the latent heat of the vapor corresponding to the tempera- ture /, 79 is the latent heat of water released on freezing. The heat C is gradually restored to the air during expansion. The pressure of the air becomes P 1? and the volume introduced into the cyl- inder is V'= 37 RtT.' The differential equation of the work is C T mdT + ^ /v n?-^= A A A Cj being the specific heat of ice, =0,5 c c, \dT dC d "^" 2 We do not know the law of relation between C and T 1? that is, how to com- municate to the air the heat released from the water and ice formed. We are forced to make a hypothesis which is not rigor- ously exact, but which is sufficiently ap- proximate. We will suppose that the transmission is proportioned to the fall of tempera- ture, and therefore that in which _/+ 79 Y iji '__rp whence we have; 38 i dT d'V integrating we get AEV ~ r~T, ~ V," , /v^+^n/r', _ v s -~-^ ( we have furthermore P o V 2 = whence T\ _ P.Y/ 7 T ~~ P V ' * - 1 - * 2 Equation 29 can then be written ; We can obtain the value of T 2 by suc- cessive approximations. An approximate value for T 2 is found to be 39 Suppose now that condensation occurs in the cooler, we find by the tables the pressure of pf of saturated vapor of temperature T/. and we can deduce the weight of the vapor condensed in the cooler. We shall have then; r=*: - 1 -] "" J-a The equations 29 and 30 apply in this case as in the preceding. The quantity of disposable negative heat is ; Q=m*c(T.-T f ) (31) since we suppose the negative heat of the snow formed to be lost. Finally the work produced by the expansion is ; (T'.-TJ-P.V, (32) or Wm= . + r) (T/ _ Ta) (38) A. If there is a condensation in the cooler, 40 we should replace ju l in equations 32 and 33 by ^ a?/. 14. The following table gives the cooling and general effect obtained from a cubic meter of air supposing a hygro- metric state of ^ and a temperature of 15. The weight of the air is then 1.* 2157 instead of 1.* 226 which is the weight of dry air at this temperature. We have also p =85. k 8 and //,= 0.* 00626. 41 uoisa-edxa ojm paiireo jo ori negat obtai No. 5 CD O5 CO oo CQ co . 1C CO O 1C GQ . jnoq jad | TH CO O iO TH i papuadxa i-H Oi CO "^ O O ^ <^i co ic co 06 as Ci 1C CO GO Ci J> TH GQ CQ O) ^H 1C CO t> iH CO* CO ^ 1C CO J>10OCO 5 Oi O5 TH CQ pam^qo Suijooo pajpdxa jo JH O"r-Tl> cTTH"o' 1 00" bC CQ CO 1C CO J> J> RIMINI Mossaidraoo Ul ainssajj rH W T "P "V TT _i_ "P />i"T^ ' i 2 (48) we also have or -^- 1 *^' 5 (49) V/ is given equations 38 and 41. Equa- tion 49 gives the value of V/'. The inlet valve being closed, the mass of air m + jj. which is at pressure P l and temperature T/" expands without gain or loss of heat since we neglect the 49 influence of the sides of the cylinder. At the end of the stroke, this volume becomes V 2 + v', its temperature T 2 and its pressure P 2 . We have then or and Equations 50 and 51 give Y 2 and T 2 if P 2 be known, or P 2 and T 2 if Y 2 is known ; this latter being the volume de- scribed by the piston of cylinder B. We have k-l T.=T">/ VP, When there is no waste space we have T 2 =- As T/" is greater than T/, it results that for a given weight of air passed through the machine, at a given working 50 pressure, that the final temperature of the expanded air would be higher, and consequently the number of negative calories produced would be less than if there had been no waste spaces. The work is equal to : W^^P^'-P^) + (P 2 -P )V 2 + ^l (P.-PJ' (52) 16. In order that the machine should work to the best advantage it is evident- ly necessary that the air should leave the cylinder at atmospheric pressure, that is, that P 2 should equal to P . There ought then to exist a certain relation between the volume of the compression cylinder V + v, the pressure in the reservoir P a and the volume of the expansion cylinder V 2 + v' which may be determined by the above equations. To fix the dimensions of a machine we may assume V + v and P 1 as given, and then deduce the value ofV f + t>'. If we make P^Pj equations 50 and 51 will become 51 and P V a =BmT 2 , whence fc_i /T/ _1P,-P. V \ VF-jfe-pT v^r; The work is or (54) This value for the work is the same as found in 7, where no waste space was allowed for ; only the final temperature T 2 being greater for the same weight and pressure, the work of the air is less. The work of the resistance of the machine is then : ^ffull^s ^ V OF THE n ' \ (UNIVERSITY) felFOE^^ -W- [!>,-,') _ TT _ TT mkc or W r -W m =-- (T.-T.'-T. The negative heat produced is Q=fn*e(T.-T,) (56) Q,-Q=W r -W m (57) The performance of the machine is T T u _ _ _ T.-T/-T. or T.-T.' _ (58) rn _ m ttr- L -\ -^o x i *i As T/" is greater than T 1? the useful effect is less than if there had been no waste space. 17. The following table exhibits the results of a machine having waste space of 4 per cent, of the volume described by the pistons. The amount of air used being a cubic meter at 15, and weighing 53 bC asioq "^ IT) -rH ?O O -H 00 1-5 CO O O aArpaga ja unoq jad o OC5^H iO OrHi> iO OO Oi 1C t> CQ i I r- 1 o o 10 os co co TH oi * 10 o 06 ci *5[IOAV i> Ci ?O T ( 1C J> C ^ o i> oo o CO C3 TH CO 00 GO OOQOCOT-HiOO ^, -^ '"* 000 CQ CQ O t> CO 1-1 i 00 O t> CO i> CO TH J> 00 TBnn 10 lowy. j-v^ .. ^OiOO55OO oo ^ o o j> oo I I I I I I I jossajdraoo uioij 54 1* 226. In the cooler the air is brought to 18. By comparing these results with those of 11, we see that the effect of waste spaces is by no means to be neglected since it results in a loss of about 100 calories for each theoretic horse power per hour. 18. We can neutralize the influence of waste space by closing the outlet valve of cylinder B before the end of the stroke, so as to compress the air in this space; the stroke of the piston being exactly determined, the air in the waste space may be brought at the opening of the inlet valve to the temperature T/ and the pressure P/. In this case the equations 34 and 43 apply without change. During the period of expansion we have: , (60) P^R/T/ whence 55 (62} The work restored by piston B is to make allowance for the compression of air in the waste space from the pressure P n to P, : 7, W - m ' P V ^_ Jr a v 2/ P ' P * V V ,./ V o V i (63) or T 2 ' being the temperature of the air in the cylinder at the moment compression commences before the end of the stroke. We have then : (UNIVERSITY) /v 56 k_ i When the machine is well regulated, the final pressure P, P and the equa- tions 63 and 64 become Wm= ^r-i (PiV/ - p v = ) + ^i p -"'^ (65) W W =^(T/-T,) and "We have also : T7 i~7. = T7 / i /,./' V / 57 We see that in equation 66 the term relating to waste spaces disappears if we make v = v'. The equation then becomes W r - W^^CW-V,') - P (V -V 2 )] The volume V a + w' is determined by means of equations 39, 41 and 67 when the pressure P l is known. Keciprocally when V , v, V 2 and v' are known (the dimensions of the machine) then V/ is readily found, and conse- quently P t and Tj, the pressure and tem- perature at the end of the stroke in cyl- inder B to insure the escape of the air at the atmospheric pressure. ** 19. It was remarked in 5 that the efficiency of the machine could be nota- bly improved by cooling the air in the interior of the compressor cylinder. This result can be accomplished, in part at least, if not completely, by means of a ject of water, such as is employed in compressed air engines. We will proceed to calculate the work necessary for the compression in this 58 particular case, neglecting the effect of waste spaces. Let m be the weight of dry air occu- pying the volume V . Let M represent the weight of water injected together with the amount of moisture in the air, and M.X the weight of the vapor at any instant. The dilatation or compression of the mixture of the vapor and air is effected in such manner as to satisfy the differ- ential equation : mcdt + M(rfy + dxp) = - APcZ V. (69) which expresses the fact that variations in the internal heat of the mixture equal the variations of work accomplished. We have also dq^zcfa c being the specific heat of water. The differential equation can then be written t= M.dxp p being the tension of the vapor, and P that of the mixture. 59 But xp=xr- dxp=dxr - Kpdxu - Kxudp. and dN^lLdxu p is the latent heat of the vapor, r is the heat of vaporization, u is the increase of volume of a kilogram of water vaporized. We know furthermore that We have then M.dxp 4- ApdV = M.dxr -- =^- M^ + AyrfV ==Md y t from which we deduce .dt c?V ^ T j xr (me + McJrp- + Arm -y- = M^ . Integrating between the limits Tj and (70) 60 V V M.x Q = and Mx 1 = '> and are very nearly the reciprocals ^^ it of the vapor densities under the pressures We have furthermore T Equation 70 will give M when T l and T are known. = mc(T T ) -j.) + BA-X.P.) + A(P, V-P Y ) or AW r = m^c(T 1 T ) + M.(qq Q + x^x^) (71) This equation gives the work of resist- ance when M has become known.* * The two equations 70 and 71, which express the re- lations between the volumes and the temperatures of a mixture of air and vapor, which is compressed or dilated, and which determine also the value of the work, are ap- plicable to the Mekarski motor. In this machine, which is designed to employ com- pressed air, the air is reheated just before it is introduced into the cylinder by being forced through water, having a temperature of 100 to 150. The cylinder then con- tains air and saturated vapor, heated to a mean tempera- ture of 100. 61 In M. Colladon's compressors, into which a spray of water is injected, the air being compressed to four atmos- pheres, the* temperature T x does not rise above 50 centigrade, the external air being about 50. We deduce then V, = 0.28429 cu. metres M =0.57212 W r = 15.291 kilogrammeters. When the compression is effected with- out external cooling, we found in 11 that the work of compression = 17.649 kilogrammeters, which shows a gain in the above process of about 13 per cent. It remains to determine W r for any pressure without any known value of T,. ' When a certain volume of air is dilated or compressed, with or without the ad- dition of heat, the relation of pressure to volume is expressed by the equation PV a = a constant. The weight M of equations 70 and 71 is then the weight of the vapor contained in air, saturated at the tempera- ture at which it leaves the hot water. 62 (73) which gives q-l log T.-log T , -p,)-log(P.-/).)' T 1 having been found by experiment, equation gives a. Making 74 P, =4 atmospheres, T 1 =323 and T = 288 we find a = 1.0912. a being thus determined equation 73 will give Mj. Only jflj being a function of T l9 the latter must be found by successive. approximation s. Equation 70 gives LroJL^ Me =0.4343 ^ To u ^* + 0.5888 m. r , U0 r l and w 2 are furnished by the tables. Finally we obtain W r by equation 71. 63 The saturated air in passing into the cooler is reduced in temperature from T, to T/, and a portion of the vapor is con- densed. The weight of vapor remaining and introduced into the expansion cylin- der is : V "=57 , being the density of the vapor cor- u \ responding to the temperature T/. We will calculate again the cooling produce by the expansion and the work as explained in 13. 20. The following table exhibits the results obtained from a cubic meter of air saturated at 15, since the sides of the compressor cylinder are covered with water. The weight of the air is l fc 021. 64 o^ui jo o *> O"? O 00 ^ obtai calo Negat unoq J9d padopAep CQ t> CO CD O -H O> . CO CO CO GQ O CO CO CO O5 CQ 7-1 SQ CO "^ iC CO 90Tra;sis9i jo CO J> iO O CO TH CQ CO 00 00 ^ CQ O5 t*" CQ CO 00 Oi t> CQ CO ^ CO O5 -rH CO 1C CO O5 O5 00 O CO ^ O5 00 O CO O CO^ O T-I i> CO O CO C3 GO ^ Ci C5 CO CO paui^qo TJ< t CQ ;no SnioS IITS jo T-i CJD T-I CO 1O CO J -+1 M jossgjdraoo UI TH W 03 CO CO rJH -^h 65 An examination of this table and a comparison with the table of 14 shows : 1st. That the injection of water into the interior of the compressor cylinder increases the efficiency 40 to 50 per cent. 2d. That the efficiency is at a maxi- mum at a pressure of 2^ atmospheres. 3d. That it diminishes, though slowly, as we vary from this pressure. 4th. That the quantity of snow or ice produced is not greater than that which comes from the moisture of the atmos- phere. The most favorable working pressure apppears to be in this case nearly 4 at- mospheres, since we obtain then a suffi- ciently good result (24 to 25 negative calories for a cubic meter of air), with a relatively good performance of 1,200 negative calories per horse-power per hour. Theoretically the injection of water into the compressor affords a great ad- vantage. But it is possible that the water resulting from the condensation of vapor in the cooler does not all remain 66 in the reservoir, but that a portion is carried mechanically into cylinder B. The results indicated above for the efficiency would in such a case be con- siderably modified, and the increase in the quantity of frozen vapor would consti- tute in practice a grave inconvenience. Experiment can alone decide this ques- tion. We have examined in the preceding pages nearly all the problems belonging to the air machine. We will pass now to the study of the second class of ma- chines, or those which transform motive force into negative heat by the employ- ment of a liquefiable gas. 21. THE principle of these machines is the same as that of the kind described in the last chapter. The gas is com- pressed, then deprived of its heat, and finally caused to expand in such a man- ner as to lower its temperature. Only in this instance the abstraction of the heat which follows the compression, has the effect to liquefy the gas, and it is the vaporization of the resulting liquid which 67 produces the lowering of the tempera- ture. When a change of volume of a satura- ted vapor is made under constant press- ure, the temperature remains constant. The addition or subtraction of heat, which produces the change of volume, is represented by an increase or a diminu- tion of the quantity of liquid mixed with the vapor. On the other hand when vapors, even if saturated, are no longer in contact with their liquids, and receive an addi- tion of heat, either through compression by a mechanical force, or from some ex- ternal source of heat, they comport themselves nearly in the same way as per- manent gases, and become superheated. It results from this property, that refrig- erating machines, using a liquefiable gas will afford results differing according to the method of working, and depending upon the state of the gas, whether it remains constantly saturated, or is superheated during a part of the cycle of working. / 22. We will suppose first that the 68 gas is constantly saturated and will examine the conditions to be fulfilled under this hypothesis, and the results that may be obtained. Employing the notation of the preced- ing chapter we will designate by m the weight of the gas employed, P 2 and T 2 , the pressure and the absolute tempera- ture of the cooled gas, P, and T/, the pressure and the absolute temperature in the condenser. The pressures P 2 and P a are deter- mined by the temperatures T 2 and T/; These are the pressures of a saturated vapor at these temperatures, and are given in Kegnault's tables. The temperature of the condenser is determined beforehand by local condi- tions. Depending on the surface, the interior of the condenser will exceed by 5 or 10 the temperature of the water furnished to the exterior. This latter will vary from 11 or 12 C the tempera- ture of water from considerable depth below the surface, to 30 or 35, the temperature of surface water in hot 69 climates. The volatile liquid employed in the machine ought not at this temper- ature to have a tension above that which can be readily managed by the appa- ratus. On the other hand if the tension of the gas at the minimum temperature is too low, it becomes necessary to give to the compression cylinder large dimen- sions, in order that the weight of vapor afforded by a single stroke of the piston shall be sufficient to produce a notably useful effect. These two conditions, to which may be added others; such as those depend- ing on the greater or less facility of obtaining the liquid, upon the dangers incurred in its use either from its inflam- mability or unhealthfulness, and finally upon its action upon the metals, limit the choice to a small number of sub- stances. The gases or vapors in use, are; Sulphuric Ether, Sulphurous Oxide, Am- monia and Methylic Ether. The fo0jrki' ^ed from ((UNIVERSITY] Vv. ^f f~\ -CP / 70 Regnault exhibits the tensions of the vapors of these four substances at differ- ent temperatures between 30 and + 40. The original tables expressed the ten- sions in millimeters of mercury. To facilitate computation, the tensions are here given in kilograms per square meter. Tempera- ture. Sulpuric Ether. Sulphur Dioxide. Ammonia. Methylic Ether. 40 7.187 35 9.302 30 3.908 11.918 7.837 25 5.082 15.120 9.736 20 917 6.519 19.003 11.992 15 1.194 8.265 23.669 14.652 10 1.541 10.366 29.225 17.765 5 1.968 12. $74 35.797 21.380 2.493 15.840 43.475 25.547 + 5 3.129 19.322 52.405 30.318 +10 3.894 23.378 62.707 35.743 +15 4.808 28.074 74.504 41.873 +20 5.891 33.474 87.925 48.755 +25 7.164 39.645 103.073 56.437 +30 8.651 46.659 120.083 64.961 +35 10.377 54.585 129.054 +40 12.367 63.496 160.112 An inspection of the table shows at once that the use of ether does not 71 readily lead to the production of low temperatures because its pressure be- comes then very feeble. The ether machine is, however, aban- doned. Ammonia on the contrary is well adapted to the production of low temper- atures ; but its elastic force is very great at temperatures from 15 to 30 which are readily produced in the condenser. It is not a good aid to the transformation of mechanical force into heat, on account of the difficulty of maintaining tight joints in the apparatus, and of the influence of waste spaces at the high pressures. Methylic ether yields low temperatures without attaining too great pressures at the temperature of the condenser. Finally, sulphur dioxide readily affords temperatures of 10 to 15 while its pressure is only 3 to 4 atmospheres at the ordinary temperature of the con- denser. These two latter substances then lend themselves conveniently for the production of cold by means of x mechanical force. 72 23. Let c be the specific heat of the liquid employed. q the quantity of heat neces- sary to raise 1 kilogram of the liquid from to T-273. /\, r, p, the total heat, the heat of vapor- ization, and the latent heat of the vapor considered at the temperature T-273. , the increase of volume of one kilo- gram of liquid vaporizing at T 273. We have by definition We will apply indices to these quanti- ties similar to those which affect the let- ter T in designating the different abso- lute temperatures. In order that the vapor be constantly saturated, it is necessary that the quanti- ties of liquid and of vapor taken into the compressor at once be such that at the end of the compression all the liquid 73 shall be vaporized and the vapor shall not be superheated. If we let x' ' 2 , represent the proportion of vapor contained in the mixture at the commencement of the inflow, the work of compression will be equal to the dif- ference in the amount of internal heat of the mixture at the beginning and end of the compression, that is to say to (?/-? 2 + P/-,). (76) As the compression follows an adia- batic curve, the quantities q f ^ q^ r\, r a , T', and T 2 bear the following relation: T'i /cc& tc ; 2 r^ r r t Ts T~ == "fr~T' 1 or more simply, TjfT "rfi *"! *-i Equation (77) will give the quantity <#'. Consequently equation (75) fur- nishes, when we know m, the volume V 2 that the piston should describe during the aspiration in order that all the liquid should be vaporized at the end of the compression; or, inversely, the weight m may be found if V 2 be given. 75 The vapor flows into the condenser where it is liquefied. The heat absorbed by the water of the condenser is Q 1 =ir' 1 (78) The liquid, then passes into the ex- pansion cylinder where it is vaporized, producing work till it attains the press- ure P 2 and the temperature T 2 of the refrigerant. At the end of the expan- sion, the weight of vapor in the mixture is mx^. The work, including the counter- pressure, and neglecting the work of introducing the liquid, p l ' ', which is very small, is ; AW m =wi(^ 1 - S r i -aj 9 r i ). (79) and the equation of the adiabatic curve is which determines x' 9 . The quantity of heat Q necessary to bring the mixture whose weight is 76 m(l # 2 ) of liquid and m# 2 of vapor to its primitive condition, in which m(l-#' 2 ) is the weight of the liquid and mx\ is the weight of the vapor, is, Q=wi(a5' s -a; 2 )r a or by reason of equations (76) and (79) Q= ^ mr\ (81) The work expended is W r W w and we have (82) The theoretic performance of the machine is a result already found in section 3, and which is identical with that at which we arrived in the case of permanent or non- liquefiable gases. 24. We will now take a numerical example, and consider the dimensions of the cylinders to be so regulated that a final temperature of 15 is obtained, the temperature of the condenser being 77 , and the volume of gas taken into the compressor at each stroke, V 2 =one cubic meter. The resolution of the above equa- tions supposes a knowledge of the values of r, q, c and u, or APw. They have been determined directly by Reg- nault for sulphuric ether, but not for sulphur dioxide, ammonia and methylic ether. Availing ourselves of the experi- ments of Regnault upon the compressi- bility of gases, we have been able to determine these quantities for sulphur dioxide and ammonia and prepare tables giving results for every five degrees from -30 to + 40. The method of calculation of these tables will be found in a note at the end of this essay. For sulphur dioxide we find, ' 1 =+18orT a =291 ,= 95.015 r= 87.23 2 = -5.4615 = 0.419 78 The table of 22 gives P 2 =8265 and ^=31170. Making the calculations indicated by the equations (77) and (80) we find ^=93.29 per cent. x z =11.90 per cent. Equation (75) gives m=2.554 kilograms. Equations (76) and (79) give AW r =27.08 whence W r =11.482 k'g'm. AW m = 1.82 whence W m = 772 k'g'm. Finally equations (78) and (81) give Q =197.56 Thus the volume described by the piston of the compression cylinder being one cubic meter, 2*, 5 54 of sulphur diox- ide working between 15 and -f 18 produce 197.50 negative calories. To effect this it is necessary to introduce into the compressor cylinder at each stroke a mixture of liquid and gas of which the proportion should be 93.29 per cent, of gas and 6.71 per cent, of liquid. 79 , We have for ammonia P z = 23669 P' 1= 82183 r,= 322.53 r\ = 301.70 w,= 28.604 APX!= 31.431 u^= 0.512 < = 0.1621 &=- 14.68 q\ = 18.696 The mean specific heat of the liquid at 0, c=1.0058. By means of these given values we find 3^ = 92.62 per cent. x\= 9.68 per cent. m= 2* .1034 AW r = 76.55 W r = 32,457 k'g'm AW m = 4.52 W m = 1,917 k'gm Q : =634.59 Q =562.56 2^.1034 of ammonia working between the same limits of +18 and 1 and with the same dimensions of compressor cylinder as before furnish 562.56 nega- tive calories per hour. . We will now consider ether. The vapor of ether, unlike steam, superheats 80 during expansion and condenses during compression. An ether machine ought, therefore, to work so that only vapor is introduced into the compressor cylinder, and not a mixture of liquid and vapor. At the end of the compression a part of the vapor becomes condensed. We shall then have #' 2 =1 and the equations above found become: 0,001\ 0,001 Q =m(l The empirical formulas established by Eegnault for the vapor of ether are : r=94,00 0,0790* 0,0008514# 2 , ^=0,52901^ + 0,0002959^. 81 and we deduce : for =15 and P 2 =1194 kilog. r,= 94963, AP A = 7,014, ^=2,491, 2,= -7.868, t=+l$, P 1 =5456, ^=92,302, ^, = 7,516, ^=9,618, c=0,5299, and we have tf= 0,736. Performing the calculations indicated, we find, ^,=17.85, Q=31 e .38, r =4.44, AW TO =0.42, The same machine working between 15 and +18, will give per cubic meter of Ammonia ...... 562.56 negative calories. Sulphur dioxide. 197.56 Sulphuric ether. 31.38 " 82 The efficiency would be 0,0184 per kilogrammeter. 25. We remark here that the positive work W m is always small compared with the negative work W,-. We can then without great loss of power simplify the machine by suppress- ing the expansion cylinder and replacing it by a simple cock so regulated as to de- liver into the cooler a quantity of liquid precisely equal to the amount admitted to the compressor to obtain the determ- ined cooling effect. The cycle of operations is not revers- ible. We shall have ^-^--SL, but AW r Q,-Q' the proportion will be less than % y T rp, _J,~ , and the efficiency would be less. * 1 ^2 This manner of working is represented in the diagram, Fig. 1, by replacing the adiabatic line V^V, by the two right lines V^V", and V'" 2 V" 2 situated to the right of the point V 2 . The quantity Q proportioned to V" 2 V is less than the 83 84 quantity Q of the preceding case which was proportioned to V 2 'V , and the quan- tity Qj Q will be augmented by a quan- tity proportional to the area V^V'^V,. The equations (76), (77) and (78) re- main unchanged. The weight m of the liquid under the pressure P 1 and the temperature T\ passing suddenly into the refrigerator, a part of the liquid is vaporized; the temperature of the mixture becomes T 2 and the pressure P 2 . The quantity cc 2 of liquid, which is vaporized, is given by the equation 0.001.ra_ n ~^~ which shows that the variation of inter- nal heat mtyzq'^+XtPs) is equal to the exterior work accomplished ; V' 2 being the volume occupied by the weight mx^ of vapor after the passage of the mixture into the refrigerant. 85 We have V' 2 =ra If we neglect the very small quantity 0.001 ra Li -~ 6~ the preceding equation becomes*: ay^'i-ft (84) The quantity Q is again given by the equation or by reason of eq. (76) Qzzmr^-AWr = C^- from whence the performance The efficiency will be less. It is easy to show that the value of x^ given by eq. (84) is always greater than that given by eq. (80). Consequently the value of Q will be less in the second case than in the first, and the ratio ^- will also be v^ y less. In applying equations (84) and (85) to the same cases as those of 24, we find for sulphur dioxide 86 cc 2 = 12.64 per cent. Q=195.71 and the performance=0. c 0170 per kilo- grammeter. For ammonia : a; 2 = 10.35 per cent. Q=558.11 and the efficiency 0. C 0172. Finally for sulphuric ether # 2 = 18.46 per cent. Q=:30.96 efficiency = Of 0164 26. In order to realize, either the cycle of Carnot or the non-reversible cycle indicated above, it is necessary, when we employ a liquefiable gas which superheats under compression, to introduce into the compressor cylinder at each aspiration, a mixture of liquid and vapor in such pro- portions that it shall all be in the state of gas at the end of the compression. We can devise no practical means of realizing this condition. So we content ourselves when employing freezing ma- chines that use a liquefiable gas, with 87 introducing- into the compressor the gas without any mixture of liquid. It hap- pens then with sulphur dioxide and am- monia that the gas superheats during com- pression,, and therefore that during a part of the operation the machine acts like the air machine. It is clear that under these conditions we augment the range of temperature between T, of the gas arriving in the con- denser, and T 2 of the refrigerant, and consequently of the useful effect of the apparatus. Referring again to Fig. 1 we see that we start with a volume V Q greater than V of the preceding case y compress the vapor to the volume v l following the adiabatic curve v v, of the superheated gas; cool it from the temperature T t to the temper- ature T/ corresponding to its liquefaction under the pressure P r It is then passed into the refrigerant either producing work and describing the adiabatic curve VjV 2 or by means of a cock by which means it describes the lines V/V,'" and V/"V./'. The quantity of negative heat gained 88 by superheating is represented by the length V v and the increase of resistant work by the area V^v^. Tracing from the point V Q the adiabatic curve of the saturated vapor, the point v/ will be to the left of v^ If the compressed vapor follows the Q' adiabatic V Q V^ the performance ^ -= ^! np and finally, ofQ=A do + vdp)-vdp + (93) 96 For the equation of an adiabatic curve, it is necessary to make dQ 0. We have then : (94) Introducing the value of T from equa- tion (86), it becomes. c v dt dp ,. c p 7m . AB~~T = p integrating |gF=3p -f const. or finally (W an equation analogous to equation (4) which we found for air. Replacing T by this value in equation (86) we get finally for the equation of the adiabatic curve AB (96) mits, for superheated steam, this equatioji be- If be equal to n, as Zeuner admits, 97 comes pv k =& constant, and it is similar to that which represents the adiabatic curve of the permanent gases. Eq. (94) gives the work of compres- sion pdo= - whence n -p] (97) or again and (99) 29. We can now establish the equa- tions relating to the compression of a liquefiable gas in a cylinder. A weight m of gas occupying the volume V 2 at the temperature T 2 , and under the pressure P 2 is compressed until the pressure is P, of the condenser. The temperature T i 98 at the end of the compression will be given by the equation (95). AB (100) and the work of compression including the flowing of the the gas is C(P-P) m is given by the equation P V V * Y Y 2 ""BT~-OPS"" 0.001 ^ + -d~ the final volume P BT CP n V V 2 * V^-LJ. 1- 2 P;BT 2 -CPJ We cool the gas in the condenser under constant pressure. The volume Y 1 becomes V/ at the moment the temper- ature becomes T/; since the gas is lique- fied we have; 99 P BT ' CP n V ' V 2 ^ i 2 P;BT 2 -CP and the quantity of heat removed from the condenser is : Q^mcp (T^T/J + mr/ (103) The volume occupied by the liquid is O.OOl.ra *,= -*- tf being the density of the liquid supposed constant. The liquid is then passed into the re- frigerant without producing work. The quantity mx^ of gas which vapor- izes while the pressure passes from P x to P 2 and the temperature from T/ to T 2 is by equation (84); mx^=m(q^-q^. The quantity of negative heat obtained is: Q=m(l-aj a )r a or Q=^(A t - ?1 ') (104) and we have or 100 We can verify the equality Q t Q= AW r or Keferring to the fundamental equa- tion and making dQ=O it becomes mc U mPdv = and consequently (P-P) (105) We have furthermore by definition, an equation which signifies that the total heat of the vapor at t is equal to the in- ternal heat ATI augmented by the ther- mal equivalent of the work of vaporiza- tion and dilatation. We have then A,-A,=C P (^-TJ-^P^-P") Hi This equation is applicable to a super- heated vapor above its point of satura- tion. 191 It applies also at the point of satura- tion ; we have then which verifies the equation Q^Q^AW,. Equation (105) can be written : C(P"-P) =0. the equation becomes C 1 If we make -~- -- =0. AB n Under this form it expresses Him's law of superheated vapors, and may be thus expressed: from the point of con densation, to the point at which the super- heated vapor possesses the same proper- ties as the permanent gases, the product pv remains constant while the internal work remains the same. But the equation 102 is not verified for the cases of the two liquefiable gases which we have studied, and consequently we cannot apply to them the law of Him. 30. We will now take a numerical example and suppose as in the preceding case, that a cubic meter of gas is admitted at the temperature of 15 under a pressure corresponding to this temper- ature, and that it is compressed until its tension is that of the condenser and that the temperature of this latter is, in the interior, +18. Sulphur dioxide. Equation (102) gives Equation (100) gives; making c p - 0.15438 after Eegnault, and = 0.211882; Cp (p \ 0.211882 =^ =334.31 or ^= Equations (103) and (104) Q=197.75 whence AW r = Q 1 Q=28.71 and W r = 121.75 and the theoretic performance =0. C 0162 or 4.374 calories per horse power per hour. In a double acting engine working at high velocity we estimate the resistances at about 15 per cent, of the power ex- pended. 1.15W r =13.998 and the performance becomes 0?0141 or 3.807 calories per horse power, per hour. This performance is double that of the machine working with dry air between the same limits of temperature. This difference shows not that the air is theo- retically a less efficient agent in the pro- duction of cold, but that to produce the same useful effect, the air machine having much larger dimensions than the liquefi- able gas machines will experience propor- tionally greater loss through resistances. 31. Generally with sulphur dioxide 104 we do not get as low a temperature as -15. The opening of the cock which leads from the condenser to the cooler is so reg- ulated that the pressure in the latter is about T 9 of an atmosphere, which corre- sponds to a temperature of 12. 41. P 2 =9301kg. 2 =-12.41. With these values the tables, given at the end of this memoir, give r 2 = 94.377 q= -4.517 1^=0.3863 and by means of equations (100), (102), (103) and (104) of 29 it is easy to cal- culate T 1? Qj, Q and W r . The results of these calculations are recorded in the following table, which gives the negative heat obtained, the work absorbed and the performance per cubic meter of sulphur dioxide, suppos- ing the apparatus regulated for a tem- perature of 1241 in the refrigerant, and that the temperature of the interior of the condenser varies from +15 to -{-40: 105 op calori ega jnoq J8d asjoq jnoq jod -, . , O5 ^ . H 00 CO tO CO TH 00 I C3 TJJ SO 00 CO O5 O 1O -^ CO CO CQ 0? TH JO QO 1C T-I t- . co 1-1 oj* co ao 10 ^ CQ ,_! T | -pH TH O oooooo o oooo oo .toooo? as as noiss9iduioo jo TH CQ TH o" A*q uosuapuoo oqi jo aa^AY 53 CO CO CO CQ T ? 'aoissaidraoo bnCO 00 rH CO O OO O O CO 00 Oi O TH r rH rH Saipuodssuoo . ^i TJI 10 O li fcpj> t- ^H 10 G o o ^ o o t jo fcj - CQ C? CO CO ^ 106 We see that the performance dimin- ishes more than one-half when the tem- perature of the interior of the condenser rises from 15 to 40. The figures of the last column do not nearly represent the number of calories really produced and utilized. It is nec- essary to take into account the loss occa- sioned by the pipes ; the waste spaces in the cylinder ; of loss of time in opening of the valves ; of the leakage around the piston and valves; of the reheating by the external air ; and finally, when ice is being made, of the quantity of the ice melted in removing the blocks from their molds. It requires about 100 calories to con- geal to 7 a kilogram of water taken at 15 or 16. Manufacturers estimate that practically the sulphur dioxide ap- paratus using water at 12 or 13, pro- duces 25 kilograms of ice, or 2,500 calo- ries per horse power per hour, measured oh the driving shaft, which is about 55 per cent, of the theoretic efficiency indi- cated above. 107 * Fig. 3 represents the Pictet machine from a design furnished us by the invent- or. It has a double-acting compression cylinder with four valves. The cylinder is furnished with a jacket, within which a current of cold water is made to circu- late. The gas is compressed to a tension corresponding to the temperature of the water employed for cooling, generally 1.8 to 2 kilograms effective pressure ; then it is discharged by the pipe T into the condenser C where it is liquefied. This condenser is like the surface condensers of marine engines. It has a surface of about 24 square meters for 100,000 theoretic calories per hour, or 48 square meters for 100,000 effective calor- ies per hour measured by the ice pro- duced. The quantity of water employed de- pends upon the difference of temperature to be allowed between the inside and outside of the condenser. If this difference is to be 5 each litre of water releases 5 calories and the 108 109 quantity of water to be employed will be for 100 theoretic calories produced , " Q which would require for the example of 31 and for a temperature of 20 in the condenser, 22.8 litres. The liquid dioxide passes into the re- frigerant K by the pipe T', the supply being regulated by the cock r so that the pressure shall be T 9 of an atmosphere in the refrigerant and 3 atmospheres in the condenser. If the outlet by*the cock be diminished the pressure is lowered in the cooler, and the temperature is also low- ered, but the useful effect also diminishes, since for the same volume described by the compressor piston, less weight of gas is used. We have in this machine, there- fore, the same facilities for varying the useful effect as in the air machines. The refrigerant is constructed like the condenser. Its surface is 29 square meters for each 100,000 theoretic neg- ative calories produced per hour. It is 110 immersed in an incongealable bath formed of a solution of calcium chloride. The temperature of the interior of the refrigerant being 12, that of the bath being 7. In this bath are immersed the tanks or moulds within which the water is frozen. Finally the sulphur dioxide returns to the compressor cylinder by the pipe T". The dioxide may be employed contin- uously so long as no air is permitted to enter the joints. Any leakage might lead to the production of the trioxide and pos- sibly sulphuric acid which would lead to injury to machine. Exceptional care is re- quired in maintaining tight joints. Some experiments with an ammonia machine have not yielded very good re- suls ; but the want of success seems to have resulted rather from an imperfect action of the surface of the refrigerant than from any inherent defect in the gas it- self. Ammonia gas prevents the advant- age of affording about three times the useful effect as sulphur dioxide for the same volume described by the piston. Ill But this advantage is balanced by the inconvenience of higher pressures and consequently more leakage, &c. Between the limits of temperature of 12.41 in the refrigerant and + 18 in the condenser we find for ammonia : 112 P 2 = 26559 kilos. r=321.06 and we have 0^=0.50836 We deduce for each cubic meter de- scribed by the piston : w=2.163 k. T 1 =342.75 1 =69.75 Q l= 709.48 Q =627.03 AW r =Q,-Q= 82.45 W r =34.959 kg. Theoretic efficiency: 0.0179 or 4.833 per horse power per hour. "Working the apparatus between 30 and +18 we find. 2 = 330.48 2 =0.9463 = -31.82 ^=388.20 ^=115.20 Q i= =370.52 Q=295.44 113 W r =31.834 Theoretic result: 0.00928 or 2505 per horse power per hour. CHAPTEK IV. MACHINES EMPLOYING CHEMICAL ACTION. 34. It remains to discuss the ice making machines which employ chemical affinity in their mode of action, and of which the ammonia machine of M. Carre is the type. Fig. 5 exhibits the disposition of the parts of this apparatus. It consists of a boiler A which contains a concentrated solution of ammonia in water; this boiler is heated either directly by a fire as shown in the figure, or indirectly by pipes leading from a steam boiler. The condenser B communicates with the upper part of the boiler by the tube aa; it is cooled externally by a current of cold water. The refrigerant C is so con- structed as to utilize the cold produced; the upper part of it is in communication with the lower part of the condenser by 114 115 means of the tube bb. The details of the construction are not shown in the figure. An absorption chamber D is filled with a weak solution of am- monia ; the tube cc puts this chamber in communication with the refrigerant C. The absorption chamber communicates with the boiler by two tubes. One dd y leads from the bottom of the boiler to the top of the chamber D; the other, ffj leads from the bottom of D to the top of the boiler. Upon the pipes ff is mounted a little pump whose use is to force the liquid from the absorption chamber where the pressure is main- tained at about one atmosphere, into the boiler, where the pressure is from 8 to 12 atmospheres. The change of temperature is managed through the attachments to the pipes /'/ and dd in a manner that will be easily comprehended by an inspection of the figure. To work the apparatus the ammonia solution in the boiler is first heated. This releases the gas from the solution 116 and the pressure rises. When it reaches the tension of the saturated gas at the temperature of the condenser, there is a liquefaction of the gas, and also of a small amount of steam. By means of the cock A, the flow of the liquefied gas into the refrigerant C is regulated. It is here vaporized by absorbing the heat from the substance placed here to be cooled. As fast as it is vaporized it is absorbed by the weak solution in D. The small quantity of watery vapor is carried along mechanically. Under the influence of the heat in the boiler A, the solution is unequally satur- ated, the stronger solution being upper- most. The weaker portion is conveyed by the pipe dd into the chamber D, the flow being regulated by the cock #, while the pump sends an equal quantity of strong solution from D back to the boiler- While these exchanges are brought about in the solutions, there is also an exchange of temperatures whereby the weak liquid arrives cold in the absorp- 117 tion chamber, and the strong solution is delivered in the boiler hot. The working of the apparatus depends upon the adjustment and regulation of the cocks g and A, and of the pump; by means of these, the pressure is varied, and consequently the temperature in the refrigerant C controlled. It is seen that the working is similar to that of the machines described in the preceding chapters. The chamber D fills the office of aspirator, and the boiler A. plays the part of compressor. The mechanical force producing ex- haustion, is here replaced by the affinity of water for ammonia gas; and the mechanical force required for com- pression is replaced by the heat which severs this affinity and sets the gas at liberty. We see then in advance that we shall again find a greater part of the equations already established in the dis- cussion of the liquefiable gas machines. 35. We will assume at first, that under the influence of the heat applied to the boiler, ammonia gas only is driven 118 off, and no steam. We will assume a certain weight of the gas to enter the boiler in a state of solution ; being heated, it will be separated from the water, requiring a certain quantity of heat which we will call Q'. ' Then, being conducted to the condenser, it will be cooled and then liquefied, and will im- part to the water surrounding the coils a quantity of heat Q,. In the refrigerant it is evaporated, borrowing from the exterior a quantity of heat Q ; it is next absorbed by the liquid in the chamber D, disengaging a certain amount of heat to the liquid (which may be deducted from the total amount required in the boiler) ; and, finally, it is reconveyed to the boiler, where it arrives in its original condition. By reason of the exchange of temperature effected at E, all the heat of the weak solution going out of the boiler, is restored to the strong solution enter- ing it, so that the changes of tempera- ture in the water are effected without expenditure of heat. In the complete cycle if we neglect the 119 small amount of work performed by the pump, and the heating and cooling due to contact with the air, it is clear that all the heat from external sources, being Q' from the boiler, and Q from the refrigerant, will be equal to the amount Qj carried away by the water of the condenser. We have then Q'=.Q t _Q and the efficiency will be expressed by which is identical Qi~ y with that found for the machines depend- ing on mechanical action. Q' the quantity of heat which it is necessary to expend in order to produce the quantity Q of negative calories, being equal to Q t Q, has the same value as the quantity AW r , the calorific equiva- lent of the mechanical work expended in the machines previously discussed, to produce this same quantity Q of negative calories. We proceed to show that be- tween the same limits of temperature in 120 the condenser and refrigerant, and for the same value of Q, the quantity Q' in this class of machines, is equal, very approximately at least, to the quantity We arrive then at this remarkable result ; that^in all the ice machines, when they work between the same limits of temperature, the theoretic quantity of negative heat produced is exactly the same for each calorie expended, whether it is directly produced by chemical ac- tion, or indirectly under the form of me- chanical work. But as a calorie represented by 424 kilogrammeters costs in the best heat motors an expenditure of at least 10 cal- ories in the fire, it would seem that the chemical machines possess a considerable advantage over all the others, since in these latter the heat is employed directly, and not under the expensive form of mechan- ical work. Practically, however, this ad- vantage is much less than that which seems to result from the above calcula- tions; as we will proceed to show. 121 36. We will assume the hypothesis mentioned in the beginning of the pre- ceding section, and determine the quan- tities Q', Q 1 and Q in terms of the tem- peratures, the pressures and weights of the gas employed. We will preserve the notations of the previous chapter. T l being the absolute temperature of the gas as it enters the condenser; T/ its absolute temperature in the condenser, and T 2 the absolute temperature in the refrigerant. Let m be the weight of the gas con- sidered, occupying the volume V 2 at the temperature T 2 , and under the pressure P 2 at its entrance into the absorption chamber. Let ATI be the internal heat at the temperature T ; qe the heat necessary to raise a kilogram of water from to 1. After the gas has been absorbed by the water, the absolute temperature of the mixture will be T' a . During the process of absorption of the gas, there is an amount of external work accomplished equal to P 2 (V 2 w), w of being the volume of water. 122 The difference in internal heat before and after this operation is equal to this external work. We have then q e \ + raATT/- q e 2 - mAU 2 =AP 2 (V 2 - w). The solution is conveyed to the boiler, and there heated until all the gas is driven off. It then occupies the volume Vj under the pressure P 1? and at the temperature T r The necessary quantity of heat Q" is equal to the difference in quantities of internal heat, augmented by the exterior work accomplished. This work is equal to PjCVj-w) less the work of the pump, (p-p>- We have then Q"=? ,-? ', + wAU.-wAU, + AP,(V->)-A(P-P>. Adding this equation to the preceding, member to member, we find This equation is established without taking account of the effect of exchange of temperature. There is furnished to the 123 solution which enters the boiler a quan- tity of heat precisely equal to q ei -^[e^ The quantity of heat Q' to be supplied by the boiler, in order to bring the pressure of the gas from P a to P J? and from the temperature T 2 to T l is then -TJ,) + AP^-AP.V, (107) The equations 101 and 105 gave, in case of compression by a mechanical force, AW r =iwA(U l -U i ) + AP.VAP.V, which is identical with the preceding. We have then Q,'=A.~W r provided that the temperature T, in the case where the change of pressure of the gas is obtained by the heat combined with the chemical action, is the same as in the case where the change is due to a mechanical force. Experiment proves that it is nearly so. It appears that the temperature to which it is necessary to heat the am- monia solution to obtain a given press- ure is higher as the solution becomes weak. Now in the ice machines the so- 124 lution conveyed to the boiler contains rather less of the gas as the pressure in the refrigerant becomes more feeble. We understand therefore how the tem- perature T x ought to increase as the tem- perature T a of the refrigerant diminishes. Unfortunately, precise experiments upon this point are wanting. A series of observations made by M. Eouart upon a Carre machine is here- with given. The first column of each table gives the absolute pressures in atmospheres and kilograms ; the second the tempera- tures observed in the boiler ; the fourth, the temperatures of water in the con- denser ; the fifth column gives the tem- peratures of the liquefied gas corre- sponding to the pressures in the first column (see table in 22); the tempera- tures are those of the interior of the condenser, and are naturally more ele- vated than the exterior. In the case of mechanical compression the final temperature T, is related to the initial temperature and to the initial 125 and final pressures as expressed by the equation (100) AB /PA c p T,=T, |BV The third column of the table gives the temperatures calculated by this for- mula, supposing T 2 =243 and P a =.ll,918. For the mean pressures the calculated temperatures coincide nearly with the observations. For the higher pressures the calculated pressures are higher fchan the observed. But it is necessary to remark that in this case the watery vapor mixed with the gas exerts a great- er influence, and that the true gas press- ures ought to be sensibly less than the pressures which have served as a basis for calculation. The condensation in the condenser and the evaporation in the refrigerant, are brought about exactly as in the case of the machines acting by mechanical force. We shall have then, as in 27, 126 Pressure in Boiler. Temperature of Boiler Atm. Kilog. Observed. Calculated Degrees. Degrees. l^j 15,501 48 2 20,668 58 $j 25,835 65 3 31,002 70 3J 36,169 75 4 41,336 80 4A 46,503 84 . 5 51,670 88 5J^ 56,837 92 6 62,004 94 gi^ 67,171 100 714" 74,921 106 106 7J<2 77,505 108 109 8 82,672 112 116 8K 87,839 116 121 9 93,006 120 127 9/<2 98,173 124 132 10 103,340 128 137 10^ 108,507 132 142 11 113,674 136 147 12 123,998 142 156 13 134,332 146 164 14 144,666 152 172 15 155,000 156 180 15 155,000 158 180 127 Temper ature of water of con- denser. Tempera- ture inside of condenser Differ- ence. Remarks. Degrees. Degrees. Degrees 9 9 9 9 9 9 9 10 10 10 15.0 16.1 5.0 \ 6.1 1 The gas liquefies and the apparatus Begins to work. 12 18.0 6.0 13 20.0 7.0 14 21.7 7.7 15 23.3 8.8 ^0 17 25.1 8.1 JT\ 17 26.7 9.7 dfa I 19 28.1 9.1 /^ * 24 31.0 7.1 /* *- 30 32.8 2.8 35 36.0 1.0 / ^/ o fiT^ 37 38.0 1.0 / ^^ to t^i 39 38.0 [ 52S r* oc **ff ** ^ 128 Absolute pressures. Temperature of Boiler Atm. Kilog. Observed. Calculated Degrees. Degrees. 3 31,002 73 &A 46,503 90 5 51,670 94 &A 56,837 100 6 62,004 103 V4 67,171 106 7 72,338 110 ^A 77,505 118 109 8 82,672 124 116 8K 87,839 130 121 9 93,006 136 127 9K 98,173 140 132 10 103,340 146 137 10% 11% 111,089 121,423 147 145 148 153 13 134,332 148 164 14 144,666 154 172 15 155,000 160 180 1% 160,167 163 180 Q=m(l - 0.001 V Q'^Q.-Q- 129 1 Temper- Tempera- ature of ture of condenser interior- of water condenser (observed), (calculat'd) Differ- ence of tempera- tures. Observations. Degrees. Degrees. Degrees. 8 8 8 8 8 9 14.1 ( The liquefied 10 ie.i 61^ gas appears. 12 18.0 e!o 14.5 20.0 5.5 15 21.7 6.7 16 23.3 7.3 17 25.1 8.1 19 27.4 8.4 16 (?) 30.4 14. 4(?) 16 (?) 32.8 16. 8(?) 35 36.0 1 38 38.0 38 40.0 1 The two following tables give the results of calculations for one cubic meter of ammonia gas, for temperatures in the condenser ranging from +15 to + 40. In the first the temperature of 130 the interior of the refrigerant is taken at - 15. In the second table it is - 30. The numbers in the last column are calculated on the supposition that a kilo- gram of coal burned yields 4000 calories. First case: $ a = 15, m=l k .932. H o> . 02 .2 ma o o ^ O II . fl 8 2 * ~ o gg O O II 02 a O K! Q3 11 si s .s| tga III ^ o PnrO * "cS *"* *c Q ^ . o 1H a 03 "IrO* y 'I ^ I* M 53 5 S< H H Q & Q o H & deg. deg. cal. cal. cal. cal. cal. 15 67.77 638.71 564.83 73.88 7,645 3<>,580 20 81.74 640.76 554.49 86.27 6,427 25,708 25 95.69 642.61 543.98 98.63 5,515 22,060 30 109.61 644.12 533.29 110.83 4,813 19,252 35 123.47 645.53 522.43 123.10 4,244 16,976 40 137.27 646.57 511.31 135.26 3,779 15,116 131 Second case: /= 30, ra=l k .023. O jg s i S ^ 5-Si IrS H 02 g O> O Q 2 CO ,__; O ^ CO J O 1C J> O i-H GO J> 00 t> J> CO ^ CQ rrt ^ CO "^ CO " ^ ^ Cf> 00 00 00 t> CO ^ 1O 1C 1C iO 1O O n^ ft CO 00 05 O ' ' p g 3 e - S ^x j L"~: S I'll . 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