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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3rg053

For a van der Waals gas expanded as $Z = 1 + B / V_{m} + C / V_{m}^{2} + \dots$ , which statements are correct?

A $B = b - a / RT$
B $C = b^{2}$
C $B$ changes sign at $T = a / R b$
D $C$ is negative at all temperatures

Answer: A, B, C

From

Z = \frac{1}{1 - b / V _{m}} - \frac{a}{RT V _{m}} = 1 + \frac{b}{V _{m}} + \frac{b ^{2}}{V _{m}^{2}} + \dots - \frac{a}{RT V _{m}}

, so

B = b - a / RT

and

C = b^{2}

(A and B true).

B = 0

when

RT = a / b

, the Boyle temperature (C true).

C = b^{2}

is always positive (D false).

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