Q. 800 cc volume of a gas having $\gamma = \frac{5}{3}$ is suddenly compressed adiabatically to 100 cc. If the initial pressure is $p$, then the final pressure will be
A) $\frac{p}{32}$
B) $\left( \frac{24}{5} \right)p$
C) $8p$
D) $32P$
Explanation
(d) For adiabatic process $pV^{\gamma} = constant$
$\Rightarrow \ \ \ \ \frac{P_{2}}{P_{1}} = \left( \frac{V_{1}}{V_{2}} \right)^{\gamma}$
$\therefore\ \ \ \frac{{\ P}_{2}}{P} = \left( \frac{800}{100} \right)^{5/3}$
$\Rightarrow \ \ \ \ \ \ \ P_{2} = 32\ P$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.