Question:
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
- \(16:1\)
- \(40:1\)
- \(32:1\)
- \(28:1\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
A sudden compression in an insulated container leaves no time for heat exchange. So the process is adiabatic: \(PV^\gamma=\text{constant}\).
Step 2: Find gamma:
For a monatomic gas, \(\gamma=\dfrac53\).
Step 3: Apply:
\[ \frac{P_2}{P_1}=\left(\frac{V_1}{V_2}\right)^\gamma=8^{5/3} \]
Step 4: Compute:
\(8^{5/3}=(8^{1/3})^5=2^5=32\).
Step 5: Choose:
The ratio is \(32:1\), option (C).
Final Answer:
The pressure rises 32 times. \[ \boxed{32:1} \]
A sudden compression in an insulated container leaves no time for heat exchange. So the process is adiabatic: \(PV^\gamma=\text{constant}\).
Step 2: Find gamma:
For a monatomic gas, \(\gamma=\dfrac53\).
Step 3: Apply:
\[ \frac{P_2}{P_1}=\left(\frac{V_1}{V_2}\right)^\gamma=8^{5/3} \]
Step 4: Compute:
\(8^{5/3}=(8^{1/3})^5=2^5=32\).
Step 5: Choose:
The ratio is \(32:1\), option (C).
Final Answer:
The pressure rises 32 times. \[ \boxed{32:1} \]
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