26 WILSON 



ART. C 



fundamental equations. For adiabatic changes de = — pdv 

 may be put in form 



Cv— = — a — , or C„ log e = — a log y + H{-n), 



€ V 



or for any change, 



de dv dH 



Cv — = — a 1 — r- dr], 



e V dt] 



which, by the equations e = Cvtfpv = at, becomes 



dH 

 de = - pdv + t—- dr] = dQ - dW = td-q - dW . 

 drj 



Hence dH/dr] = 1 and H = r] -\- const; with the constant taken 

 as Cj, log Cv this makes* 



Cv log — = 77 — a log y , 



the equation between e, rj, v. 

 Lecture XIV. The differential de = tdr] — pdv gives 



(de\ _ /de\ _ _ ^ _ /dt\ _ _ /dp\ 



\dr]/^ ' \dv/^ ' d'r]dv \dv/ ^ \dr]/^ 



Consider the functionf \p = e — trj and d\p = —rjdt — pdv. 

 Then 



\dt/,~ '^' \dv/ ~ ^' dtdv ~ \dv)t ~ \dt/,' 



* On comparison with the development, Gibbs, I, 12-13, formulas A 

 to D, it will be seen that there are slight differences, but the method here 

 given was followed by Gibbs in his course on thermodynamics in differ- 

 ent years. 



t I do not recall, and there is no evidence in the notes, that Gibbs 

 gave names to the functions ^p, x, f such as free energy, heat function, 

 or thermodynamic potential. He appears not to have referred to the 

 function * = 77 — (c + pv)/t = — f/< which is widely used as a potential. 



