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JEE Advanced levelSingle correct optionDifficulty 3 of 3rg208

For a van der Waals gas, the ratio $\frac{P _{c} V _{c}}{T _{c}}$ in terms of $R$ is

A $\frac{3 R}{8}$
B $\frac{8 R}{3}$
C $R$
D $\frac{27 R}{8}$

Answer: A

P_{c} V_{c} = \frac{a}{27 b ^{2}} \times 3 b = \frac{a}{9 b}

and

R T_{c} = \frac{8 a}{27 b}

. Dividing,

\frac{P _{c} V _{c}}{R T _{c}} = \frac{a /9 b}{8 a /27 b} = \frac{3}{8}

, so

\frac{P _{c} V _{c}}{T _{c}} = \frac{3 R}{8}

.

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