Question

A polyatomic gas at pressure P, having volume 'V' expands isothermally to a volume '3 V' and then adiabatically to a volume '24 V'. The final pressure of gas is (for moderate temperature changes)

• A. 16 P
• B. 24 P
• C. P / 36
• D. P / 48

Hint:

For polyatomic gases, the ratio of specific heats $\gamma \approx 1.33$ or $4/3$.

Answer 1

The Correct Option is D

Step 1: Isothermal Expansion
$P_1V_1 = P_2V_2 \Rightarrow P \cdot V = P_2 \cdot 3V \Rightarrow P_2 = P/3$.
Step 2: Adiabatic Expansion
For polyatomic gas, $\gamma = 4/3$ (standard assumption).
$P_2V_2^\gamma = P_3V_3^\gamma \Rightarrow (P/3) \cdot (3V)^{4/3} = P_3 \cdot (24V)^{4/3}$
Step 3: Calculation
$P_3 = (P/3) \cdot (\frac{3V}{24V})^{4/3} = (P/3) \cdot (\frac{1}{8})^{4/3}$
$P_3 = (P/3) \cdot (2^{-3})^{4/3} = (P/3) \cdot 2^{-4} = \frac{P}{3 \times 16} = \frac{P}{48}$
Step 4: Conclusion
The final pressure is $P/48$.
Final Answer:(D)