Question

A monatomic gas is suddenly compressed to 1/8th of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is ($\gamma =$ 5/3)

• A. 32
• B. 16
• C. 2
• D. 64

Answer 1

The correct option is A 32

In an adiabatic process $P{V}^{\gamma }=constant$
$\therefore P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$ .....(1)
Given $\gamma =\frac{5}{3}$
$V_2=\frac{V_1}{8}$
substituting $V_2$ in eqn(1) $P_1{V}_1^{\frac{5}{3}}=P_2(\frac{V_1}{8}{)}^{\frac{5}{3}}$
$\Rightarrow P_2=32P_1$