Kinetic Theory - Result Question 30
30. 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
[2013]
(a) $\frac{R}{(\gamma-1)}$
(b) $\frac{(\gamma-1)}{R}$
(c) $\gamma R$
(d) $\frac{1+\gamma}{1-\gamma}$
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Answer:
Correct Answer: 30. (a)
Solution:
- (a) $C_p-C_v=R \Rightarrow C_p=C_v+R$
$\because \gamma=\frac{C_p}{C_v}=\frac{C_v+R}{C_v}=\frac{C_v}{C_v}+\frac{R}{C_v}$
$\Rightarrow \gamma=1+\frac{R}{C_v} \Rightarrow \frac{R}{C_v}=\gamma-1$
$\Rightarrow C_v=\frac{R}{\gamma-1}$
