The molar specific heat of an ideal gas at constant pressure and constant volume is…
The molar specific heat of an ideal gas at constant pressure and constant volume is $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{v}}$ respectively. If $\mathrm{R}$ is universal gas constant and $\gamma=\frac{C_p}{C_y}$ then $C_v=$
$\frac{1-\gamma}{1+\gamma}$
$\frac{1+\gamma}{1-\gamma}$
$\frac{\gamma-1}{\mathrm{R}}$
$\frac{\mathrm{R}}{\gamma-1}$
Solution
$C_p-C_v=R$
Dividing both the sides by $\mathrm{C}_{\mathrm{v}}$,
$\begin{array}{ll}
\therefore & \gamma-1=\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}} \\
\therefore & \mathrm{C}_{\mathrm{v}}=\frac{\mathrm{R}}{\gamma-1}
\end{array}$