Question:
A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If \(γ = 1.5\), then the increase in the temperature of the gas in Kelvin is (\(γ\) is the ratio of specific heats)
A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If \(γ = 1.5\), then the increase in the temperature of the gas in Kelvin is (\(γ\) is the ratio of specific heats)
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Use T V^(gamma - 1) = constant with normal temperature taken as 273 K.
Updated On: Oct 1, 2026
- \(273\)
- \(373\)
- \(473\)
- \(573\)
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The Correct Option is A
Solution and Explanation
Step 1: Adiabatic Relation:
For a sudden (adiabatic) compression, \(T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}\).
Step 2: Substitute:
Normal temperature is taken as \(T_1=273\) K. With \(V_2=V_1/4\) and \(\gamma=1.5\):
\[ T_2=T_1\left(\frac{V_1}{V_2}\right)^{\gamma-1}=273\times4^{0.5}=273\times2=546\ \text{K} \]
Step 3: Increase:
\(T_2-T_1=546-273=273\) K.
Step 4: Check the Other Options:
373, 473 and 573 K would need final temperatures of 646, 746 and 846 K, i.e. factors of 2.37, 2.73 and 3.10, which do not equal \(4^{0.5}=2\). So (A) is correct.
Final Answer:
The temperature rises by 273 K, option (A). \[ \boxed{\text{(A) } 273} \]
For a sudden (adiabatic) compression, \(T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}\).
Step 2: Substitute:
Normal temperature is taken as \(T_1=273\) K. With \(V_2=V_1/4\) and \(\gamma=1.5\):
\[ T_2=T_1\left(\frac{V_1}{V_2}\right)^{\gamma-1}=273\times4^{0.5}=273\times2=546\ \text{K} \]
Step 3: Increase:
\(T_2-T_1=546-273=273\) K.
Step 4: Check the Other Options:
373, 473 and 573 K would need final temperatures of 646, 746 and 846 K, i.e. factors of 2.37, 2.73 and 3.10, which do not equal \(4^{0.5}=2\). So (A) is correct.
Final Answer:
The temperature rises by 273 K, option (A). \[ \boxed{\text{(A) } 273} \]
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