Q. During an adiabatic process, the pressure $p$ of a fixed mass of an ideal gas changes by $\mathrm{\Delta}p$ and its volume $V$ changes $\mathrm{\Delta}V$. If $\gamma = C_{p}/C_{v}$, then $\mathrm{\Delta}V/V$ is given by
A) $- \frac{\mathrm{\Delta}p}{p}$
B) $- \gamma\frac{\mathrm{\Delta}p}{p}$
C) $- \frac{\mathrm{\Delta}p}{\gamma p}$
D) $- \frac{\mathrm{\Delta}p}{\gamma^{2}p}$
Explanation
(c) $K_{a} = \gamma p = - \frac{\mathrm{\Delta}p}{\mathrm{\Delta}V/V}$
$\therefore\ \frac{\mathrm{\Delta}V}{V} = - \frac{\mathrm{\Delta}p}{\gamma p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.