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JEE Main levelSingle correct optionDifficulty 2 of 3rg084

Which of the following is the correct relation among the critical temperature $T_{c}$ , Boyle temperature $T_{B}$ and inversion temperature $T_{i}$ of a van der Waals gas?

A $T_{c} < T_{B} < T_{i}$
B $T_{B} < T_{c} < T_{i}$
C $T_{i} < T_{B} < T_{c}$
D $T_{c} < T_{i} < T_{B}$

Answer: A

T_{c} = 8 a /27 R b = 0.296 a / R b

,

T_{B} = a / R b

and

T_{i} = 2 a / R b

. Hence

T_{c}

is lowest, then

T_{B}

, then

T_{i}

:

T_{c} : T_{B} : T_{i} = 8 : 27 : 54

.

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