The pressure and volume of an ideal gas are related as PV3/2 = K (Constant). The work done when the gas is taken from state A (P₁, V₁, T₁) to state B (P₂, V₂, T₂) is: (a) 2(P₂√(V₂) - P₁√(V₁)) (b) 2(√(P₁) V₁ - √(P₂) V₂) (c) 2 (P₂V₂ - P₁V₁) (d) 2 (P₁V₁ - P₂V₂)

Answer: (d). For PVx = K: W = (P₁V₁ - P₂V₂)/(x - 1). Here x = 3/2, so x - 1 = 1/2. W = 2(P₁V₁ - P₂V₂) So the answer is (d).

The pressure and volume of an ideal gas are related as PV3/2 = K… | JEE Main 2024 (1 Feb, Shift 1)

Q130JEE Main 2024 · 1 FEB · SHIFT 1Medium

Thermodynamic Processes

The pressure and volume of an ideal gas are related as $PV^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state $A\,(P_1, V_1, T_1)$ to state $B\,(P_2, V_2, T_2)$ is:

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Answer: (d)

For $PV^{x} = K$ : $W = \frac{P_1V_1 - P_2V_2}{x - 1}$ .
Here $x = \frac{3}{2}$ , so $x - 1 = \frac{1}{2}$ .
$W = 2(P_1V_1 - P_2V_2)$
So the answer is (d).

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