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JEE Main levelSingle correct optionDifficulty 2 of 3rg203

If the critical pressure of a gas is $P_{c}$ and the critical volume is $V_{c}$ , the van der Waals constant $a$ equals

A $3 P_{c} V_{c}^{2}$
B $P_{c} V_{c}^{2}$
C $27 P_{c} V_{c}^{2}$
D $\frac{P _{c} V _{c}^{2}}{3}$

Answer: A

V_{c} = 3 b

gives

b = V_{c} /3

, and

P_{c} = a /27 b^{2} = a /27 (V_{c} /3)^{2} = a /3 V_{c}^{2}

. Hence

a = 3 P_{c} V_{c}^{2}

.

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