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The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$, respectively. If $\gamma = \frac{C_P}{C_V}$ and R is the universal gas constant, then $C_V$ is equal to:
A
$\gamma R$
B
$\frac{1 + \gamma}{1 - \gamma}$
C
$\frac{R}{(\gamma - 1)}$
D
$\frac{(\gamma - 1)}{R}$
Detailed Solution
$C_P - C_V = R$ and $\gamma = \frac{C_P}{C_V}$
$\gamma C_V - C_V = R \Rightarrow C_V = \frac{R}{\gamma - 1}$
$\gamma C_V - C_V = R \Rightarrow C_V = \frac{R}{\gamma - 1}$