Q. If $\gamma$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by
A) $\frac{R}{\gamma - 1}$
B) $\frac{\gamma R}{\gamma - 1}$
C) $\gamma R$
D) $\frac{(\gamma - 1)R}{\gamma}$
Explanation
(a) $\frac{C_{P}}{C_{V}} = \gamma \Rightarrow C_{P} = C_{V}.\gamma\ But\ C_{P} - C_{V} = R$
$\Rightarrow C_{P} = R + C_{V}$
$\therefore\gamma C_{V} = C_{V} + R \Rightarrow C_{V}(\gamma - 1) = R \Rightarrow C_{V} = \frac{R}{\gamma - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.