JEE Main 2025 Apr 8 Shift 2, Physics Q11: Thermodynamic Processes

JEE Main2025Apr 8, Shift 2Physics

A monoatomic gas having $γ = \frac{5}{3}$ 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 and initial pressure is:

( $γ$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

A
$16$
B
$40$
C
$32$
D
$28$

Solution

Sudden compression of a thermally insulated gas is an adiabatic process, obeying $P V^{γ} = constant$ .

Therefore $\frac{P _{f}}{P _{i}} = (\frac{V _{i}}{V _{f}})^{γ}$ .

With $V_{f} = V_{i} /8$ , the ratio $V_{i} / V_{f} = 8$ ; substituting: $\frac{P _{f}}{P _{i}} = 8^{5/3}$ .

Since $8 = 2^{3}$ , we have $8^{5/3} = 2^{5} = 32$ , matching option (3).

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JEE Main 2025 Apr 8 Shift 2, Physics Q11: Thermodynamic Processes

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