Question

If a gas of volume $400~\text{cc$ at an initial pressure $P$ is suddenly compressed to $100~\text{cc}$, then its final pressure is (The ratio of specific heats $\gamma = 1.5$)}

• A. $\dfrac{P}{32}$
• B. $8P$
• C. $32P$
• D. $16P$

Hint:

Use $P_1V_1^\gamma = P_2V_2^\gamma$ for adiabatic processes when $\gamma$ is given.

Answer 1

The Correct Option is B

For adiabatic process: $PV^\gamma = \text{constant}$
$\Rightarrow P_f = P_i \left( \dfrac{V_i}{V_f} \right)^\gamma = P \left( \dfrac{400}{100} \right)^{1.5} = P \cdot 4^{1.5}$
$4^{1.5} = \sqrt{4^3} = \sqrt{64} = 8 \Rightarrow P_f = 8P$