Question

A monoatomic gas $(\gamma =\frac{5}{3})$ is suddenly compressed to $\frac{1}{8}$ of its original volume adiabatically, then the pressure of the gas will change to.

• A. times its initial pressure
• B. 8 times its initial pressure
• C. times its initial pressure
• D. 32 times its initial pressure

Answer 1

The correct option is D

32 times its initial pressure

$P{V}^{\gamma }=constant$

$\Rightarrow \frac{P_2}{P_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma }\Rightarrow P_2=(8{)}^{\frac{5}{3}}{P}_1=32P_1$