JEE Main · 2023 · 29 Jan 2023 · Shift 1 · States of Matter

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For 1 mol of gas, the plot of pV vs p is shown below. p is the pressure and V is the volume of the gas.

What is the value of compressibility factor at point A ?

(A) $1 - \frac{a}{RTV}$ ✓ Correct
(B) $1 + \frac{b}{V}$
(C) $1 - \frac{b}{V}$
(D) $1 + \frac{a}{RTV}$

Answer: (A)

Solution

Writing

p V = Z R T

for one mole, the height of the curve measures the compressibility factor. At point A the curve has dipped below its ideal, horizontal value, so

Z < 1

, the regime in which intermolecular attraction dominates. For such a gas the van der Waals treatment gives

Z = 1 - \frac{a}{R T V}

, the attractive term pulling

Z

beneath unity. The compressibility factor at A is

1 - \frac{a}{R T V}

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Single correct option

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