Question

A monoatomic gas at pressure $P_1 $ and volume $V_1 $ is compressed adiabatically to $\frac {1}{8}^{\text{th}} $ of its original volume. What is the final pressure of the gas ?

• A. $64P_1$
• B. $P_1$
• C. $16P_1$
• D. $32P_1$

Answer 1

Answer: (D)

Ideal gas equation, for an adiabatic process is
$P V^{\gamma}=$ constant or $P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}$
For monoatomic gas $\gamma=\frac{5}{3}$
$\therefore P_{1} V_{1}^{5 / 3}=P_{2}\left(\frac{V_{1}}{8}\right)^{5 / 3}$
$\Rightarrow P_{2}=P_{1} \times(2)^{5}=32 P_{1}$