Problem $2\mathrm{.}4$ Relationship between isentropic and isothermal compressibility $($problem $3\mathrm{.}8$

Ragone$)$

Derive an expression for the isentropic compressibility of a solid $({}_s)$ in terms of isothermal

compressibility $({}_T)$ and other properties normally tabulated.

${}_S-=-\frac{1}{V}(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{P}}{)}_S$

${}_T-=-\frac{1}{V}(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$

$[$Hint: Derive the expression of ${}_S$ as a function of ${}_T,C_v$ and $C_p]$