Question:easy
A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to \((\frac{1}{8})^{th}\) of its initial volume. The ratio of final pressure to initial pressure is
A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to \((\frac{1}{8})^{th}\) of its initial volume. The ratio of final pressure to initial pressure is
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Adiabatic: P V^gamma = constant, gamma = 5/3.
Updated On: Oct 1, 2026
- \(16:1\)
- \(40:1\)
- \(32:1\)
- \(28:1\)
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: Use the relation:
$P_1V_1^\gamma=P_2V_2^\gamma$ with $V_2=V_1/8$.
Step 2: Rearrange:
$P_2=P_1\cdot8^\gamma$.
Step 3: Evaluate:
$\gamma=5/3$ gives $8^{5/3}=32$. Option (C).
Final Answer:
8 to the power 5/3 is 32. \[ \boxed{C} \]
$P_1V_1^\gamma=P_2V_2^\gamma$ with $V_2=V_1/8$.
Step 2: Rearrange:
$P_2=P_1\cdot8^\gamma$.
Step 3: Evaluate:
$\gamma=5/3$ gives $8^{5/3}=32$. Option (C).
Final Answer:
8 to the power 5/3 is 32. \[ \boxed{C} \]
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