Question

A gas for which $\gamma =1.5$ is suddenly compressed to $\frac{1}{4}$ th of its initial value then the ratio of the final to initial pressure is

• A. 1:16
• B. 1:8
• C. 1:4
• D. 8:1

Answer 1

The correct option is D 8:1

Suddenly compressed implies adiabatic process
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
$\frac{P_1}{P_2}={\left(\frac{V_2}{V_1}\right)}^{\gamma }={\left(\frac{V/4}{V}\right)}^{1.5}=\frac{1}{4^{3/2}}=\frac{1}{8}$
$\frac{P_2}{P_1}=\frac{8}{1}$
Option D.