62 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The value of h for a perfect gas may be found from the second of the 

 above conditions, equation (21). For a perfect gas, according to the 

 definition of fugacity, 



\p = P, and therefore 



, (9RT\u^\ {9RT\nP\ 



h = \~-rr^) P = \--^T-)r RlxlP ' (22) 



We see, therefore, that the value of /* which satisfies the condition of 

 equation (21) is expressed by a far simpler function than entropy is. 

 Let us see whether this value for the perfect gas is consistent with the 

 other condition that, 



dh= ± dS. 



For a perfect gas the following equations for isothermal change are 

 familiar : 



dQ Pdv vdP RdP __ 1 _ 



and from equation (22), 



d h = R d In P, hence, for constant temperature, 



dh = — dS, (23) 



and the condition is satisfied. The value R In P satisfies both the above 

 conditions for h in the case of a single state, the perfect gas. Moreover, 

 every substance is capable of being brought into the state of a perfect 

 gas isothermally by evaporation and indefinite expansion. Consequently 

 it is easy to show that for any state of a substance either of the two 

 conditions will define a value of h which is consistent with the other 

 condition. Thus by the first condition, expressed now by equation (23), 

 the difference in value of h between two states of a substance is equal to 

 the difference in entropy and opposite in sign, that is, 



h, — /?2 == iJ-2 — *^1* 



If we choose as the second state the vapor of the substance at such a 

 low pressure, P 2 , that the vapor may be regarded as a perfect gas, 

 h 2 = R In P 2 , from equation (22), and the last two equations give, 



h 1 = Ss-Si + BlnP* (24) 



in which *^ 2 represents the entropy of the vapor at pressure P 2 . This 

 equation furnishes a complete definition of the value of h for any state. 

 Let us see whether this value satisfies the other condition of equation 

 (21). 



