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JEE Main levelSingle correct optionDifficulty 2 of 3rg126

For a van der Waals gas at very high pressure (where $a / V_{m}^{2}$ is negligible compared with $P$ ), the compressibility factor is

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

Answer: B

Neglecting the attraction term,

P (V_{m} - b) = RT

, so

P V_{m} = RT + P b

and

Z = 1 + P b / RT

.

Z

then grows linearly with pressure with slope

b / RT

.

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