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JEE Main levelSingle correct optionDifficulty 2 of 3rg148

The critical temperature and critical pressure of a gas are $T_{c}$ and $P_{c}$ . In terms of these, the van der Waals constant $a$ is

A $\frac{27 R ^{2} T _{c}^{2}}{64 P _{c}}$
B $\frac{R T _{c}}{8 P _{c}}$
C $\frac{64 P _{c}}{27 R ^{2} T _{c}^{2}}$
D $\frac{8 P _{c}}{R T _{c}}$

Answer: A

From

T_{c} = 8 a /27 R b

and

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

:

b = R T_{c} /8 P_{c}

, and substituting into

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

gives

a = 27 P_{c} (\frac{R T _{c}}{8 P _{c}})^{2} = \frac{27 R ^{2} T _{c}^{2}}{64 P _{c}}

.

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