STRAINED ELASTIC SOLIDS 447 



Thus 



dv(t, v) dp(t, v) 



But by (41) 



dv dt 



_ dyjt, v) 

 '" ~ ^ dv 



(43) 



Therefore 



dp(t, v) 

 h = i -^' (44) 



the well known relation connecting the latent heat of change of 

 volume at constant temperature with the temperature coeffi- 

 cient of pressure at constant volume. Also from (41) we 

 derive 



dCyjt, v) _ ± ( dv(t, v) \ 

 dv ~ dv { dt j 



= t 



dtdv 



But by (43) 



Hence 



d^vjt, v) _ d^pjt, v) 



dtdv ~ df^ 



dc,{t, v) ^ d'pjt, v) 



which is another well-known relation. 



If we choose we can take the temperature and pressure as the 

 thermodynamical variables. We then write 



dv(.t, p) = — ^ — dt + — ^ — dp, (46) 



where Cp and Ip are the specific heat at constant pressure and the 



