$8-11.$ In this problem you will derive the equation $($Equation $8\mathrm{.}24)$

$C_P-C_V=-T(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{T}}{)}_P^2(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{V}}{)}_T$

To start, consider $V$ to be a function of $T$ and $P$ and write out $dV.$ Now divide through by $dT$ at constant volume $)=(0$ and then substitute the expression for $(del\frac{P}{d}$elT${)}_V$ that you obtain into Equation $8\mathrm{.}23$ to get the above expression.