344 KEYES ART. J 



and substitution in [11] leads to a relation in which the variables 

 separate. Integration then results in equation [255]. Evidently 

 since c, except for the monatomic gases, is in general a quite 

 complex function of the temperature it is not practical to write 

 t as a function of the energy in a fundamental equation* in the 

 variables energy, entropy and volume. f If c is taken as a 

 function of temperature, f{t), the equation for the entropy may 

 be readily obtained from [11] for 



de + pdv fit)dt + pdv 



<'" = — r~ = — i — 



or 



fit) -j + alogv + H. (3) 



The forms of f{t) which are known, as for hydrogen, make it 

 practically impossible to eliminate t to give an equation in 

 the variables e, rj and v. 



9. Constants of Energy and Entropy. The remarks following 

 equation [255] are important, for the assigning of the constants 

 of entropy, H, and of energy, E, is a matter of importance in all 

 cases of chemically interacting components. The conventions 

 which have been used are, however, somewhat varied; thus 

 Lewis and Randall ^^ define a standard state in terms of unit 

 fugacity of the elements; and 0° on the absolute or Kelvin scale 

 and one atmosphere ^^ has also been proposed. There is much 

 advantage ^^ in adopting the actual state of the gas at 0° and 

 one atmosphere, but any of the proposed systems is a possible 

 one so long as interest centers on the treatment of ordinary 

 chemical reactions by the two empirical principles of thermo- 

 dynamics. J 



* See footnote, Gibbs, I, 88. 



t Gibbs has discussed the advantages of volume and entropy as inde- 

 pendent variables (Gibbs, I, 20). 



t The statistical mechanics analogue of the entropy may for example 

 be easily computed from equation [92] of Gibbs' Statistical Mechanics 

 (Gibbs, II, Part 1, 33) for the simple case of a gas assumed to be composed 

 of structureless mass points. Before making the computation, note 

 should be taken of the fact that equation [92] may be dimensionally 

 satisfied by dividing the right hand member under the logarithm by 

 Planck's constant h raised to the 3nth power. 



