Q. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of the absolute temperature. The ratio $\frac{C_{p}}{C_{v}} = \gamma$ for the gas is
A) 2
B) 3/2
C) 5/3
D) 4/3
Explanation
(b) In an adiabatic process, $pV^{\gamma} =$ constant
Put $V = \frac{RT}{p}$
$\frac{pR^{\gamma}T^{\gamma}}{p^{\gamma}} =$constant
$\therefore p^{1 - \gamma}T^{\gamma} =$constant
$p \propto T^{\gamma/\gamma - 1}$
$\therefore\ \frac{\gamma}{\gamma - 1} = 3$
$3\gamma - 3 = \gamma$
$2\gamma = 3$
$\gamma = \frac{3}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.