Question

The molar specific heat of an ideal gas at constant pressure and constant volume is '$C_p$' and $C_v$' respectively. If 'R' is the universal gas constant and the ratio of $C_p$ to $C_v$ is ${}^{\prime }{\gamma }^{\prime }$ then $C_v$ =

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

Answer 1

The correct option is D $\frac{R}{\gamma -1}$

Given that,

$\frac{C_p}{C_v}=\gamma$

$⟹C_p=\gamma .C_v$

And, $C_p-C_v=R$

$\gamma C_v-C_v=R$

$⟹(\gamma -1)C_v=R$

$⟹C_v=\frac{R}{\gamma -1}$

Hence, the answer is option - (D).