1-1 PBOCEEDINGS OF THE AMERICAN ACADEMY. 



V 



P = T ; f - . . (28) 



il v a 1 



From equation (9\ siuce -, " = 0, — . ... < =0, and therefore the 



il v a 1 



term is independent of the temperature when r r is independent 



of the volume. Thia term represents the heal developed in the free 

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

 increases witb increasing volume,- — -thai is, when there is a cooling 

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

 pressui 



Sine is a function of the volume alone, we may write equation 



(23) iu the form, 



'-(?-'<•>>-£■ 



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 arc constants. (25 



This equation has been proved experimentally i>\ Ramsay and Young.* 



dUS, 

 The values of ' for a few may be found from the por< 



plug experiments of Joule and Thomson. These experimenters d< 



mined directly, not , , hut - , , and found thai in all their ex peri- 

 ay d ]> 



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

 quantity was independent of the actual pressure of the experim 



dtyi 



That is, at constant temperature —7— is a constant. "\\ e may write 



dp 



dv = - Jr/ ,1 P 



from the gas law, neglecting the errors introdi d 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, 



* Zdt. Phys. Chem., I. 483. 



