Question

A monoatomic gas at pressure $P_1$ and $V_1$ is compressed adiabatically to ${\left(\frac{1}{t}\right)}^{th}$ its original volume. What is the final pressure of the gas?

• A. ${\text{16 P}}_1$
• B. ${\text{32 P}}_1$
• C. ${\text{P}}_1$
• D. ${\text{64 P}}_1$

Answer 1

The correct option is B ${\text{32 P}}_1$

For adiabatic process,
$P_1{V}_1=P_2{V}_2$
$P_1{V}^{5/3}=P^{\prime }{\left(\frac{V}{8}\right)}^{5/3}$
$P^{\prime }=P_1(8{)}^{5/3}$
$P^{\prime }=P_1\times 2^5$
$P^{\prime }=32P_1$
Hence, option $\left(D\right)$ is correct.