ON THE SIGNIFICANCE OF THE FORGOTTEN 

 THERMODYNAMIC THEOREMS OF CARNOT 



I. Introduction 



EXAMINATION OF THE famous memoir by Nicolas-Leonard-Sadi Carnot (1796- 

 1832) entitled Reflexions siiv la Puissance Motrice du Feu et sur les Ma- 

 chines propres a Developper celte Puissance (A Paris, chez Bachelier, libraire, 

 Quai des Augustins, No. 55, 1824)* shows that this work, ahhough in the form 

 of a single chapter without subheadings, falls naturally into three distinct 

 parts. 



In the first part {Ca pp. 1-38, Ma pp. 3-21) Carnot describes the cycle and 

 demonstrates the theorem which have both come to bear his name. As is well 

 known, Carnot's demonstration consists of a logically correct argument from 

 two premises, one of which is true and the other false: the true premise is the 

 impossibility of perpetual motion, and the false one the caloric theory of heat, 

 according to which heat is a weightless indestructible substance. Carnot's 

 theorem is thus an outstanding example of a physically true statement which 

 is rigorously deducible from premises which are at least partly false. 



In the second part (Ca pp. 39-88, Ma pp. 21-46) of the Reflexions, Carnot 

 deduces seven further theorems relating mostly to the thermal behavior of 

 gases, and illustrates these theorems to some extent by numerical data and 

 calculations. It is these seven theorems that we here refer to as "the forgotten 

 thermodynamic theorems of Carnot." The arguments by which Carnot arrives 

 at these theorems are again logically correct and again based upon two prem- 

 ises, one of which is true and the other false: the true premise here is Carnot's 

 theorem and the false one again the caloric theory of heat. In the light of 

 modern knowledge it is obvious that any theorem deduced in this way must 

 belong to one of the following three classes: class A, theorems based on Car- 

 not's theorem alone and therefore true; class B, true theorems based either 

 on the caloric theory alone or on the caloric theory and Carnot's theorem 

 simultaneously; class C, false theorems based either on the caloric theory alone 

 or on the caloric theory and Carnot's theorem simultaneously. Class B would 

 evidently furnish further examples of true statements rigorously deducible 

 from premises at least partly false. 



In the third part {Ca pp. 89-1 18, Ma pp. 47-61) of his memoir Carnot com- 

 pares in the light of the two preceding parts the practical advantages of differ- 



* The first edition of this work will here be referred to bv the abbreviation Ca. An English 

 translation with a few notes by W. F. Magie is included, together with writings by Claiisius 

 and by William Thomson, in volinnc VI of "Harper's Scientific Memoirs" (ed. by J. S. Ames; 

 New York and London: 1899); this volume, which is entitled The Second Law of Thermo- 

 dynamics, will here be referred to by the abbreviation Ma. An annotated German translation 

 of the Reflexions by Wilhelm Ostwald, containing further bibliographic information on Car- 

 not, constitutes Nr. 37 of "Ostwald's Klassiker der Kxakteu Wissenschaften" (Leipzig: 1892). 



c -^77 : 



