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JEE Main levelSingle correct optionDifficulty 2 of 3rg190

Which of the following is the correct expression for the inversion temperature of a van der Waals gas?

A $T_{i} = \frac{a}{R b}$
B $T_{i} = \frac{2 a}{R b}$
C $T_{i} = \frac{8 a}{27 R b}$
D $T_{i} = \frac{a}{2 R b}$

Answer: B

The Joule-Thomson coefficient of a van der Waals gas at low pressure is

μ = \frac{1}{C _{p}} (\frac{2 a}{RT} - b)

, which vanishes when

T = 2 a / R b

. This is the inversion temperature, twice the Boyle temperature.

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