Q. For a certain gas, the ratio of specific heats is given to be $\gamma = 1.5.$ For this gas
A) $C_{V} = \frac{3R}{J}$
B) $C_{P} = \frac{3R}{J}$
C) $C_{P} = \frac{5R}{J}$
D) $C_{V} = \frac{5R}{J}$
Explanation
(b) $C_{P} - C_{V} = \frac{R}{J} \Rightarrow C_{P} = \frac{R}{J} + C_{V} = \frac{R}{J} + \frac{R}{J(\gamma - 1)}$
$\Rightarrow C_{P} = \frac{R}{J}\left( \frac{\gamma}{\gamma - 1} \right) = \frac{R}{J}\left( \frac{1.5}{1.5 - 1} \right) = \frac{3R}{J}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.