] 90 Dr. Schroeder van der Kolk on Gases, 



§ VIII. Conclusion. 



The following remarks may be made in conclusion. In defi- 

 ning an ideal gas, in § I. only has it been assumed that k is con- 

 stant. This is enough where it is only a question of deviations 

 from Mariotte and Gay-Lussac's law ; and the deduction of the 

 absolute zero depends on no further assumption. But where 

 the specific heat is concerned, it must be defined more accurately 

 whether the gas in expanding is to perform internal work or not. 

 The assumption that in this gas no internal work is performed 

 is at the basis of the definition of Carnot's function of tempera- 

 ture. Upon this depends the further development of the theory, 

 and its application to bodies occurring in nature. 



An ideal gas, therefore, must satisfy the three following condi- 

 tions : k is independent of pressure and temperature, and per- 

 forms in expanding no internal work. Now Cohen-Stuart has 

 shown* that the second condition follows from the first and 

 third; the assumption, therefore, that a gas satisfies the first and 

 third but not the second, is self-contradictory. If there were an 

 ideal gas, the question would soon be settled ; but as this is not 

 the case, the question is, whether an ideal gas as defined above 

 can occur ; or whether perhaps it is not in contradiction with 

 other natural laws, whether known or unknown to us. If the 

 mechanical theory of heat is to be developed in accordance with 

 fact and not as a mere play of formulae, it is of the greatest im- 

 portance to investigate this as accurately as possible. 



It frequently occurs that in an analytical investigation a new 

 magnitude is introduced to simplify calculation ; this obtains its 

 significance from its definition, and is without influence on the 

 results of the theory. This is the case, for instance, with the 

 potential function. Now the assumption of an ideal gas mate- 

 rially simplifies the development of the mechanical theory of 

 heat ; but in the present case this is neither sufficient nor is it 

 the chief question. If the theory is to be developed in accord- 

 ance with fact, it must start from premises which occur in nature, 

 and not from such as are arbitrarily excogitated by us. Hence 

 the ideal gas is only another name for the condition to which, 

 according to our idea, one or more gases approximate. The 

 occurrence of this condition has never been experimentally 

 proved, and it is only from the known properties of gases that 

 we can conclude with greater or less certainty that there is such 

 a condition. We know that at a low pressure and high tempe- 

 rature the deviations from the ideal condition are small, but this 

 is by no means adequate for a firm establishment of the theory. 

 It may readily be imagined that in applying this theory to gases 

 * Poggendorff's Annalen, vol. cxix. p. 327. 



