A monoatomic gas having $\gamma=\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Heat & Thermodynamics

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✓ Correct
(D)28

Answer: (C)

Solution

For a sudden compression in a thermally insulated container the process is adiabatic, so

P V^{γ}

stays constant and

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

. With the volume reduced to one-eighth and

γ = \frac{5}{3}

, this is

8^{5/3} = (2^{3})^{5/3} = 2^{5}

. The ratio of the final to the initial pressure is

32

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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