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) 273 (b) 373 (c) 473 (d) 573

Answer: (a). Sudden compression is adiabatic: T₂ = T₁((V₁)/(V₂))γ - 1 = T₁(4)0.5 = 2T₁. Normal temperature T₁ = 273 K, so T₂ = 546 K. Rise = 546 - 273 = 273 K So the answer is (a) 273.

A gas at normal temperature is suddenly compressed to one-fourth of… | MHT CET 2026 (19 Apr, Shift 1)

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Thermodynamic Processes

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$ , then the increase in the temperature of the gas in Kelvin is ( $\gamma$ is the ratio of specific heats)

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Answer: (a)

Sudden compression is adiabatic: $T_2 = T_1\left(\frac{V_1}{V_2}\right)^{\gamma - 1} = T_1(4)^{0.5} = 2T_1$ .
Normal temperature $T_1 = 273\text{ K}$ , so $T_2 = 546\text{ K}$ .
Rise $= 546 - 273 = 273\text{ K}$
So the answer is (a) 273.

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