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JEE Advanced levelSingle correct optionDifficulty 3 of 3rg153

Which of the following is a correct expression for the gas constant $R$ in terms of the van der Waals critical constants of a gas?

A $R = \frac{8 P _{c} V _{c}}{3 T _{c}}$
B $R = \frac{3 P _{c} V _{c}}{8 T _{c}}$
C $R = \frac{P _{c} V _{c}}{T _{c}}$
D $R = \frac{27 P _{c} V _{c}}{8 T _{c}}$

Answer: A

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

for a van der Waals gas, so

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

. Using experimental critical constants this gives a value of

R

about 20 to 30 percent too high, which reveals the limitation of the equation.

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