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JEE Main levelSingle correct optionDifficulty 2 of 3rg071

For a van der Waals gas at low pressure (neglecting $b$ ), the compressibility factor is

A $Z = 1 + \frac{a}{RT V _{m}}$
B $Z = 1 - \frac{a}{RT V _{m}}$
C $Z = 1 + \frac{P b}{RT}$
D $Z = 1 - \frac{P b}{RT}$

Answer: B

At low pressure

V_{m} - b \approx V_{m}

, so

(P + \frac{a}{V _{m}^{2}}) V_{m} = RT

, giving

P V_{m} = RT - \frac{a}{V _{m}}

. Dividing by

RT

:

Z = 1 - \frac{a}{RT V _{m}}

, which is less than 1.

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