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JEE Main levelSingle correct optionDifficulty 2 of 3rg145

For a van der Waals gas the critical temperature is

A $\frac{a}{R b}$
B $\frac{8 a}{27 R b}$
C $\frac{a}{27 b ^{2}}$
D $\frac{27 a}{8 R b}$

Answer: B

Solving

(\partial P / \partial V_{m})_{T} = 0

and

(\partial^{2} P / \partial V_{m}^{2})_{T} = 0

gives

V_{c} = 3 b

,

T_{c} = 8 a /27 R b

and

P_{c} = a /27 b^{2}

. The expression

a / R b

is the Boyle temperature.

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