Question

For an ideal gas $\frac{C_p}{C_v}=\gamma$. then its specific heat capacity at constant volume $\left(C_v\right)$ is :

• A. $\frac{R}{(\gamma -1)}$
• B. $\frac{1}{R(\gamma -1)}$
• C. $\frac{\gamma R}{(\gamma -1)}$
• D. $\frac{R}{\gamma (\gamma -1)}$

Answer 1

The correct option is A $\frac{R}{(\gamma -1)}$

Given that

$\frac{C_P}{C_V}=\gamma$ ----- (1)

We know that

$C_p-C_v=R$ ------ (2)

Dividing both side by $C_v$, we get -

$\frac{C_p}{C_v}-1=\frac{R^{}}{C_v}$

$\Rightarrow \gamma -1=\frac{R^{}}{C_v}$ Since, $[\frac{C_p}{C_v}=\gamma ]$

$\Rightarrow C_v=\frac{R^{}}{(\gamma -1)}$

$\therefore$ (A) option is correct.