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JEE Main levelSingle correct optionDifficulty 2 of 3rg048

For a van der Waals gas, the second virial coefficient in the expansion $Z = 1 + B / V_{m} + \dots$ is

A $B = a - \frac{b}{RT}$
B $B = b - \frac{a}{RT}$
C $B = \frac{a}{RT} - b$
D $B = ab / RT$

Answer: B

Writing

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

and expanding

\frac{1}{1 - b / V _{m}} \approx 1 + b / V_{m}

gives

Z \approx 1 + \frac{1}{V _{m}} (b - \frac{a}{RT})

, so

B = b - a / RT

.

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