STRAINED ELASTIC SOLIDS 449 



the change of entropy is equal, by equation (41), to 



- < Cv{t, v)dt + U{t, v) — ^ dt V 

 It is also, by (46), equal to 



- Cp{t, v)dt. 

 Equating these two expressions we obtain the result 



Cp{t, p) = Cv(t, v) + U{t, v) — ^^' 

 and using (44) we arrive at 



In exactly the same manner we can derive the equations 

 which connect the thermal and mechanical properties of a 

 solid. For the sake of brevity we shall write eQ, f) and 7?(^ /) 

 for e{t,fi, . . . /e) and 7?(i, /i, ... /e); so that when we write, for 

 example, 



dyjt, f) drjjtj) 

 or ' 



we mean the temperature variation of t? at constant strain or the 

 rate of variation of r] with respect to /r, the temperature and the 

 five strain functions other than /r being maintained constant. 

 In analogy with (41) we write 



dv(t,f) = ^ * + S '-^ if- (52) 



The summation extends over six terms; c is the specific heat at 

 constant strain of the solid (per unit volume as measured in the 

 state of strain), which means that the solid is prevented from 

 changing volume and shape. The six quantities Ir are various 

 latent heats of change of strain; in each case the temperature 



