Q. A gas for which $\gamma = 1.5$ is suddenly compressed to the $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is
A) $1:6$
B) $1:8$
C) $1:4$
D) $8:1$
Explanation
(d) Here, $\gamma = 1.5,\ V_{2} = \frac{1}{4}V_{1};\ \frac{p_{2}}{p_{1}} = ?$
As compression is sudden/adiabatic,
$\therefore\ \ p_{2}V_{2}^{\gamma} = p_{1}V_{1}^{\gamma}$
$\frac{p_{2}}{p_{1}} = \left( \frac{V_{1}}{V_{2}} \right)^{\gamma} = (4)^{1.5} = 8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.