Question

The molar specific heat capacity of an ideal gas, at constant pressure and at constant volume, are denoted by $C_p\text{and}{C}_v$, respectively. If $\gamma =\frac{C_p}{C_v}\text{and R}$ 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

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

$C_p-C_v=R$

$\Rightarrow \frac{C_p-C_v}{C_v}=\frac{R}{C_v}$

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

$\gamma -1=\frac{R}{C_v}(\because \gamma =\frac{C_p}{C_v})$

$\therefore C_v=\frac{R}{\gamma -1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.