JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Heat & Thermodynamics

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A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

(A)P
(B)8 P
(C)32 P✓ Correct
(D)64 P

Answer: (C)

Solution

Constant entropy implies an adiabatic process. For an adiabatic process,

P V^{γ} = constant

, where

γ = \frac{5}{3}

for a monoatomic gas.

Given

V_{2} = \frac{V _{1}}{8}

P_{1} V_{1}^{5/3} = P_{2} (\frac{V _{1}}{8})^{5/3}

P_{2} = P_{1} \times 8^{5/3} = P_{1} \times (2^{3})^{5/3} = P_{1} \times 2^{5} = 32 P_{1}

The answer is (C) 32 P.

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Single correct option

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