Question:
A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressures is nearly equal to
A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressures is nearly equal to
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A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressures is nearly equal to
Updated On: Apr 15, 2026
- 5
- 6.5
- 7
- 3.5
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Sudden expansion implies an adiabatic process where $PV^{\gamma} = \text{constant}$.
Step 2: Adiabatic Index
Given $C_V = 2R$, then $C_P = C_V + R = 3R$. $\gamma = \frac{C_P}{C_V} = \frac{3R}{2R} = 1.5$.
Step 3: Calculation
$\frac{P_1}{P_2} = \left(\frac{V_2}{V_1}\right)^{\gamma} = (3)^{1.5} \approx 5.1$.
Final Answer: (A)
Sudden expansion implies an adiabatic process where $PV^{\gamma} = \text{constant}$.
Step 2: Adiabatic Index
Given $C_V = 2R$, then $C_P = C_V + R = 3R$. $\gamma = \frac{C_P}{C_V} = \frac{3R}{2R} = 1.5$.
Step 3: Calculation
$\frac{P_1}{P_2} = \left(\frac{V_2}{V_1}\right)^{\gamma} = (3)^{1.5} \approx 5.1$.
Final Answer: (A)
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