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JEE Advanced levelSingle correct optionDifficulty 3 of 3rg194

Assertion (A): The inversion temperature of a van der Waals gas is twice its Boyle temperature. Reason (R): Both temperatures are proportional to $a / b$ for a given gas. Choose the correct option.

ABoth A and R are true and R is the correct explanation of A
BBoth A and R are true but R is not the correct explanation of A
CA is true but R is false
DA is false but R is true

Answer: B

T_{B} = a / R b

and

T_{i} = 2 a / R b

, so A is true. R is also true, but proportionality to

a / b

alone does not fix the factor 2; that comes from the specific derivation of the Joule-Thomson coefficient. So R is not the explanation of A.

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