IN 
 
 George Davidson 
 
 Q1 1 
 
 Professor of Geography 
 University of California 
 
THE FALLACY 
 
 OF THE 
 
 SECOND LAW OF THERMODYNAMICS 
 
 AND THE 
 
 Feasibility of Transmuting Terrestrial 
 Heat Into Available Energy 
 
 An addendum to essay on 
 Means for Transmuting Terrestrial Heat 
 into Available Energy" 
 
 Read July 2, 1902, at the Pittsburg Meeting of the " Physical Section' 
 of the American Association for the Advancement of Science. 
 
 BY 
 
 JACOB T. (WAINWRIGHT 
 
 CIVIL ENGINEER 
 
 CHICAGO 
 
 1902 
 
,','.: 
 
 Qjif^j^o^ 
 
PREFACE. 
 
 It is hoped that the most exacting critic will ap- 
 preciate that the writer has herein succeeded in 
 presenting this comparatively unexplored subject 
 in a simple manner free from all questions of quan- 
 tative analysis and unknown and doubtful matter. 
 
 ABSTRACT. 
 
 In order to prove the feasibility of utilizing common omni- 
 present terrestrial heat as a substitute for fuel, it has been 
 necessary to establish three new and important truths or advance- 
 ments in the Science of Thermodynamics : 
 
 FIRST: Refutation, or destruction of the Second Law of 
 Thermodynamics. 
 
 SECOND: Establishment of a new Thermodynamic principle. 
 
 THIRD : Applying this new principle, so as to dispense 
 with the external refrigerating medium which has 
 heretofore been indispensable to the operation of 
 all motive power heat engines- 
 
THE FALLACY 
 
 OF THE 
 
 Second Law of Thermodynamics 
 
 AND THE 
 
 Feasibility of Transmuting Terrestrial 
 Heat Into Available Energy 
 
 The Second Law of Thermodynamics was promulgated by 
 Sadi Carnot, in the year 1824:. Was mathematically established 
 by Professors Clausius and Thompson (Lord Kelvin), independ- 
 ently by each, respectively in the years 1850 and 1851, on the 
 same peculiar foundation (on laws which are now obsolete) and at 
 a date when the laws of Boyle, Gay-Lussac, and Watt were con- 
 sidered sufficiently accurate and applicable to all fluids within 
 practical limits of temperature and pressure. And both investi- 
 gators were particular to explain that the mathematical treatment 
 and conclusions therefrom were based upon this assumption, which 
 was only approximately correct at best, and applied only to 
 limits of pressure and temperature that were then considered 
 practicable; (Memoirs by Carnot, Clausius, and Thompson) 
 (Translation by Professor Magie, of Princeton University; Har- 
 per & Bros., Publishers, New York, 1899). 
 
 Subsequently (in the year 1881), Professor Amagat demon- 
 strated that the laws of Boyle and Gay-Lussac are very far from 
 being true when the fluid's condition is near the critical-point. 
 Also, recent progress in the art of liquefying gases at low tem- 
 peratures has demonstrated that practical limits of temperature 
 and pressure have increased to such an extent that the critical- 
 point of many gases is readily attained. Consequently the Boyle 
 and Gay-Lussac law must be abandoned, and Amagat's principle 
 must be substituted. Thus the Thompson and Clausius assump- 
 tion is no longer applicable, and their demonstration is destroyed. 
 
 Amagat's demonstration of the impotency of the Boyle and 
 Gay-Lussac law has been universally accepted, but the effect of 
 his demonstration upon the establishment of the Second Law of 
 Thermodynamics has not before been observed. 
 
2.00 
 
 Atm. P. 25 50 
 
 100 
 
 125 
 
 150 175 
 
 200 
 
 225 250 
 
 Fig. 6. 
 
 Figure 6 is an exact reproduction of a diagram of isother- 
 nials relating to carbon-dioxide, made by Amagat (Annales de 
 Chimie et de Physique, 6e Serie, t. xxix. 1893) (Translation by 
 Professor Bams, of Brown University; Harper & Bros, publish- 
 ers, New York, 1899) and is the result of actual research. The 
 abscissas represent the pressures in atmospheres, while the ordi- 
 nates represent the corresponding values of the product resulting 
 from multiplying the pressure by the corresponding volume, oth- 
 erwise designated as pv. 
 
 The lowest isothermal shown by Amagat corresponds to the 
 temperature of zero (274 degrees absolute) on the Centigrade-ther- 
 mometer. Above the critical-pressure, and within the limits of his 
 diagram, this isothermal is practically a straight line which, if pro- 
 longed, passes through the origin of ordinates. This shows that, 
 within these limits of pressure, this particular isothermal has con- 
 stant volume for all degrees of pressure. Consequently, at or near 
 this particular finite temperature, and within these limits of 
 pressure, this particular fluid (carbon-dioxide) becomes hxnhi1,hj 
 incompressible or inert, as regards the influence of pressure alone. 
 Thus, this tiii]H>rf<iiif phenomenon is placed beyond dispute. 
 
zro. 
 
 ZOO. 
 
 v$ 
 
 / 00. 
 
 -100 
 
 Fig. 7. 
 
 This phenomenon does not result as an erratic change in the 
 condition of the fluid, but is the result of a series of gradual and 
 well known changes. For the purpose of showing this matter in 
 a more familiar way, I have constructed the diagram of isother- 
 mals shown by Figure 7, from matter shown in Figure 6. In 
 Figure 7, the ordinates represent the pressures in atmospheres, 
 while the abscissas represent the corresponding volumes. 
 
 The Second Law of Thermodynamics has been defined in 
 many different ways; all of which are merely mathematical de- 
 ductions from the fundamental law which defines, "Difference of 
 
1>< in-, , ,) ////// two Isodiabatics" as a particular thermal prop- 
 erty of a substance, which rcimiinx c<mxf<n<t for <iU f< mj>< r<itnr< *. 
 
 Also, "Difference of Entropy between two Isodiabatics" may 
 be defined as the quantity of latent-heat or heat absorbed (or 
 given up) at constant temperature, ratioed or divided by the cor- 
 responding absolute-temperature, and comprised between limits 
 defined by the two particular isodiabatics considered. 
 
 Again, thermodynamic changes or lines are said to be isodia- 
 batic to each other, when they are identical as regards tempera- 
 ture changes and transfer of heat. 
 
 Referring to Figure 7, it will be observed that such 
 "Difference of Entropy," measured on any isothermal whose 
 temperature is appreciably greater than 274 degrees of absolute- 
 temperature, will consist of a finite quantity of latent heat ratioed 
 or divided by a finite absolute-temperature, and consequently 
 there results a finite value. Whereas, if measured on the 
 isothermal corresponding to 274 degrees of absolute-tempera- 
 ture; by reason of the incompressible or inert condition acquired 
 by the fluid at or near this particular temperature, it will 
 consist of an infinitely small quantity of latent-heat ratioed or 
 divided by the very finite temperature of 274 degrees, and conse- 
 quently there results a value which is zero. Thus, in a 
 simple manner; free from all questions of quantative analysis, 
 and unknown and doubtful matter; the Second Law of Thermo- 
 dynamics is disproved, as regards its application to carbon- 
 dioxide, because this law requires one finite value for all tem- 
 peratures.""" 
 
 From the relation between Entropy and the Second Law of 
 Thermodynamics, it will be observed that such law does not per- 
 mit the inert condition (which is identical with the disappearance 
 of that property by which latent-heat can be developed), until 
 the fluid has been cooled to an extent corresponding to zero of 
 absolute-temperature. Whereas, Amagat, by his research work 
 on other gases, has conclusively demonstrated that the properties 
 of carbon-dioxide are typical for all fluids. Consequently, all 
 gases become inert at some fin <f< absolute-temperature, and there- 
 fore the Second Law of Thermodynamics is fallacious for all 
 fluids. 
 
 After having disposed of the Second Law of Thermodynam- 
 ics, my next object is to establish the principle that, it is possible, 
 in a j" /.A'/ thermodynamic engine, to change or transform the 
 pressure condition or tension of the working fluid; without trans- 
 
f err ing heat to, or from an external medium; without transferring 
 dynamic energy to, or from an external source; and without re- 
 sulting a changed temperature. 
 
 My principle indirectly conflicts with the Second Law of 
 Thermodynamics, as will appear hereinafter. 
 
 Seal,./ Volume. 
 
 Figures 1, 2, 3, and 4 show successive operations of an ideal 
 type of transforming engine. 
 
 A and B are insulated cylinders; each closed by its respect- 
 ive piston; and separated, one from the other by the diaphraui 
 D capable of a perfect conduction of heat. 
 
 The cylinder A contains the gas to be treated or transformed 
 as regards its tension, the gas in the cylinder B is merely :i 
 working fluid. By reason of the diaphram D, these separated 
 gases always have a common temperature. 
 
 Figure 5 is a Clapeyron diagram showing the successive 
 operations in the respective cylinders. 
 
 Figure 1 shows the beginning of the operation. Starting 
 with the gas in the cylinder A, in the condition at a on the dia- 
 gram; and with the gas in the cylinder B, in the condition shown 
 at e\ each gas having the same temperature but differing as re- 
 gards pressure and density. 
 
The first operation consists in densifying the gas in cylinder 
 A, through a falling range of temperature; and at constant pres- 
 sure somewhat above, or at the critical pressure; until the inert 
 condition is reached. At the same time, the gas in cylinder B is 
 expanded at a sufficient rate to maintain the above mentioned 
 constant pressure in cylinder A by reason of a transfer of heat 
 through the diaphram D. Figure 2 shows the position of the 
 pistons at the close of this operation, and the points I and /on 
 the diagram show the respective condition of these separated 
 gases after having thus passed through the series of conditions 
 shown respectively by the lines a-~b and e-f. By reason of 
 Amagat's principle, the gas in cylinder A has now acquired an 
 incompressible condition, as regards the influence of pressure 
 alone. 
 
 The second operation consists in applying an increased pres- 
 sure on the fluid in cylinder A, while the condition of the gas in 
 the cylinder B is maintained without change. Figure 3 shows 
 the unchanged position of the pistons at the close of this opera- 
 tion, and the points c and / on the diagram show the respective 
 condition of the separated gases after the gas in cylinder A has 
 thus passed through the series of conditions shown by the line 
 'ta?, while the condition of the gas in cylinder B remains 
 unchanged. 
 
 The third operation consists in densifying the gas in the 
 cylinder B, through a series of conditions exactly the reverse of 
 that by which it was expanded; at the same time, the gas in 
 cylinder A is expanded through a range of increasing tempera- 
 tures and a series of pressures suited to maintain the gas in 
 cylinder B through its return series of conditions, or in other 
 words, expanded on the line <-<! which is isodiabatic to the line 
 a-ft. Figure 4 shows the position of the pistons at the close of this 
 operation, and the points d and e on the diagram show the 
 respective condition of the separated gases after having thus 
 passed through the series of conditions shown respectively by the 
 lines c-d &u<lf-e. 
 
 These three operations cause the transformation of the gas 
 in cylinder A, from the condition of tension shown at ^, to the 
 increased tension shown at d; also cause both gases to return to 
 their initial condition as regards temperature. Whereas, the gas 
 in cylinder B is caused to depart from and return to its initial 
 
 10 
 
condition in all respects; depart and return through one range or 
 path of conditions; and consequently without a transfer of 
 heat through the diaphram D, in an aggregate sense, or in other 
 words, the heat transferred from cylinder A is returned to it 
 again. 
 
 Since this change has been effected by a return to the initial 
 condition of temperature, and without an aggregate transfer of 
 heat through the diaphram D; it necessarily results that, in an 
 aggregate sense, neither heat nor dynamic energy has been 
 transferred to, or from either cylinder. 
 
 The isothermal a-d can be chosen at sufficient temperature 
 to insure that, within the limits of the diagram, it is practically 
 governed by the law of Boyle and Gay-Lussac. In such case, 
 the return of the treated gas to its initial temperature means a 
 return to its initial condition as regards conserved energy; and 
 consequently, in order not to conflict with the First law of Ther- 
 modynamics, the area a-b-g-n which represents the external work 
 accompanying the compression, must be equal to the area c-d-m-g 
 which represents the external work accompanying the expansion; 
 from which it results that, the point d must be at a higher pres- 
 sure than the point a. 
 
 After having demonstrated the truth of my principle, my 
 next object is to show how such principle can be applied as a 
 means for dispensing with a refrigerating medium, in the opera- 
 tion of a perfect heat engine. 
 
 Again referring to Figures 1 to 5 inclusive; a modification 
 of the apparatus may readily be conceived, by which the trans- 
 formed fluid at the condition corresponding with the point d, may 
 be transferred to another cylinder capable of effecting an 
 isothermal-expansion from the condition at d to the condition at 
 a by means of heat received from an external source, and then 
 returning the fluid to the transforming engine to there be trans- 
 formed to its initial condition at d in the manner just described. 
 
 Such operation constitutes a cycle which may be successively 
 repeated. And it will be observed that; such cycle absorbs heat 
 from an external source, at a constant temperature; converts all 
 of this heat into available dynamic energy; and does not dis- 
 charge any heat to an external source. 
 
 Thus, is presented the long sought feasibility of converting 
 Terrestrial Heat into Available Energy. 
 
 11 
 
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