Question

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} $

Answer 1

Answer: (C)

Using
$C_{P}-C_{V}=R$
$\Rightarrow C_{V}\left(\frac{C_{P}}{C_{V}}-1\right)=R$
$(\gamma-1)=\frac{R}{C_{V}}$
$\left(\because \frac{C_{p}}{C_{V}}=\gamma\right)$
or $C_{V}=\frac{R}{(\gamma-1)}$