The initial pressure and volume of an ideal gas are P 0 and V 0. The final pressure of the gas when the gas is suddenly compressed to volume V₀/4 will be: (Given γ = ratio of specific heats at constant pressure and at constant volume) (a) P 0 (4) (1)/(γ) (b) P 0 (c) 4P 0 (d) P 0 (4) γ

Answer: (d). Sudden compression has no time for heat exchange: adiabatic, PVγ = constant. P₀V₀γ = P(V₀/4)γ P = P₀(4)γ So the answer is (d) P₀(4)γ.

The initial pressure and volume of an ideal gas are P 0 and V 0. The… | JEE Main 2023 (13 Apr, Shift 2)

Q142JEE Main 2023 · 13 APR · SHIFT 2Easy

Thermodynamic Processes

The initial pressure and volume of an ideal gas are P $0$ and V $0$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be:

(Given $\gamma$ = ratio of specific heats at constant pressure and at constant volume)

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Answer: (d)

Sudden compression has no time for heat exchange: adiabatic, $PV^{\gamma}$ = constant.
$P_0V_0^{\gamma} = P\left(\frac{V_0}{4}\right)^{\gamma}$
$P = P_0(4)^{\gamma}$
So the answer is (d) $P_0(4)^{\gamma}$ .

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