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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 $\gamma$ then. $C_v=$
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Verified Answer
The correct answer is:
$\frac{R}{\gamma-1}$
Using
$\begin{aligned} & C_p-C_v=R \\ & \Rightarrow C_p\left(\frac{C_p}{C_v}-1\right)=R \\ & (\gamma-1)=\frac{R}{C_v}\left(\because \frac{C_p}{C_v}=\gamma\right)\end{aligned}$
Or
$C_v=\frac{R}{(\gamma-1)}$
$\begin{aligned} & C_p-C_v=R \\ & \Rightarrow C_p\left(\frac{C_p}{C_v}-1\right)=R \\ & (\gamma-1)=\frac{R}{C_v}\left(\because \frac{C_p}{C_v}=\gamma\right)\end{aligned}$
Or
$C_v=\frac{R}{(\gamma-1)}$
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