Thermodynamics, 5th Edition

(1.15.10)

where Eq. (1.15.6) was introduced on the right. As was emphasized in connection with the third law, any adiabatic change in deformation coordinates results in a change of temperature unless phase transitions are involved. Equations (1.15.9) and (1.15.10) show the extent of such a change in terms of quantities that are experimentally accessible.

The variation of heat capacity with pressure¹ or volume at constant composition is given by ${\partial }^{2}S/\partial T\partial P=(1/T){(\partial C_P/\partial P)}_T=-{({\partial }^{2}V/\partial T^2)}_P$, whence

${(\partial C_P/\partial P)}_T=-T{({\partial }^{2}V/\partial T^2)}_P,$ (1.15.11)

(1.15.11)

and similarly ...