JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Heat & Thermodynamics

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

γ =

ratio of specific heats at constant pressure and at constant volume)

(A) $P_{0} (4)^{\frac{1}{γ}}$
(B) $P_{0} (4)^{γ}$ ✓ Correct
(C) $P_{0}$
(D) $4 P_{0}$

Answer: (B)

Solution

A sudden compression is an adiabatic process, governed by

P V^{γ} = constant

. Thus

P_{0} V_{0}^{γ} = P_{2} (\frac{V _{0}}{4})^{γ}

, which gives

P_{2} = P_{0} \cdot 4^{γ}

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Single correct option

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