Question

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

Answer 1

The correct option is D 8 : 1

Here $\gamma =1.5,V_2=\frac{1}{4}{V}_1$
As compression is sudden / adiabatic
Therefore $p_2{V}_2^{\gamma }=p_1{V}_1^{\gamma }$
$\frac{p_2}{p_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma }=(4{)}^{1.5}=8$