450 RICE 



ART. K 



and five strain-quantities are unchanged. A well-known 

 illustration can be given of the idea involved here. When one 

 extends a piece of rubber suddenly, it rises in temperature. 

 Thus if one wished to maintain the temperature constant one 

 would have to extend slowly and take heat from the solid, which 

 shows that the Ir coefficients for rubber are negative. The en- 

 ergy relation (40) is now written 



deitj) = tdriitj) + i:Xr{t, f)dfr, (53) 



and from it we derive the differential equation for Gibbs' \p 

 function, viz., 



dKtJ) = -n{t,f)dt + XXr(t,f)dfr, (54) 



where 



\p = € — tr]. 

 From (54) we derive 



driitj) dXritJ) 



But by (52) 



dfr dt 



a.(^/) 



(55) 



dfr 



Therefore 



lr= -t —^' (56) 



There are of course six equations of the type (56), and they 

 connect the heat required to maintain the temperature constant 

 when the strains are altered with the variations of stress re- 

 quired to maintain the strains constant (i.e., to prevent expan- 

 sion and change of shape) when the temperature alters. To 

 continue, from (52) we derive 



dcjtj) ^ d^tj) , 

 dfr dtdfr 



