IJ: PEOCEEDINGS OF THE AMERICAN ACADEMY. 



V dv dv ^ '' 



'.'dm' 

 d 



From equation (9), since -^-^ = 0, — , r„ ^ = 0, and therefore the 

 ^ ^ d V d 1 



term — — is independent of the temperature when c„ is independent 



of the volume. This term represents the heat developed in the free 

 expansion of a gas, and shows that when the internal energy of a gas 

 increases with increasing volume, — that is, when there is a cooling 

 effect on free exjjansion, — the gas will have lower than normal 

 pressure. 



Since —p^ is a function of the volume alone, we may write equation 

 (23) in the form, 



^ = (I- -('■))-- ^- (-) 



And since -^ — is not a function of the temperature, the equation of 

 a gas at constant volume, the " isochore," is, 



p ^^ A T — B, where A and B are constants. (25) 



This equation has been proved experimentally by Ramsay and Young.* 

 The values of ~— for a few gases may be found from the porous 



plug experiments of Joule and Thomson. These experimenters deter- 



• ^ ^- 1 dm , dm T ^ 1 T . „ , . 



mmed directly, not --. — , but — — , and lound that in all their experi- 

 ments with a variety of gases and mixtures of gases that the latter 

 quantity was independent of the actual pressure of the experiment. 



dm 



That is, at constant temperature — — is a constant. We may write 



from the gas law, neglecting the errors introduced by the deviations from 

 this law, which are of much smaller order than the errors of the experi- 

 mental results that we are using. Then, 



* Zeit. Phys. Chem., I. 433. 



