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JEE Main levelSingle correct optionDifficulty 2 of 3rg159

Which of the following gives the second virial coefficient of a gas that obeys $P (V_{m} - b) = RT$ exactly?

A $B = 0$
B $B = b$
C $B = - b$
D $B = b^{2}$

Answer: B

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

, so

B = b

and

C = b^{2}

. With no attraction term,

B

is positive at every temperature.

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