STRAINED ELASTIC SOLIDS 451 



But by (55) 



dtdfr dt^ 



Hence we obtain the six relations 



It is, of course, open to us to choose as thermodynamic 

 variables the temperature and the six components of stress. 

 The energy and entropy are then expressed in full by the 

 symbols €{t, Xi, ... Xe) and r](t, Xi, ... Ze) or briefly €{t, X) 

 and r](t, X). The entropy equation then becomes 



at, X) s;^ Lrjt, X) 



7]{t, X) = — ^ — dt -]- 2j — ~t — ' ^ 



where C is the specific heat at constant stress, i.e., under prac- 

 tically the usual conditions of measurement, where the external 

 forces on the solid are unchanged. Li, ... Le are six latent 

 heats of change of stress, each one at constant temperature and 

 with five of the stress-components unaltered. 



The energy differential equation is once more adapted to the 

 choice of variables by using Gibbs' f function, viz., 



€ — ^77 — 2 XtSt. 



Thus 



d^{t, X) = —n{t, X)dt - Xfr{t,X)dXr. (59) 



From (59) we derive 



dr){t, X) ^ dfrjt, X) 



dXr dt 



But by (58) 



dv(t, X) 



(60) 



Lr = t 



dXr 



