The value of critical temperature in terms of van der Waals' constant a and b is given by (a) TC = (8a)/(27Rb) (b) TC = (27a)/(8Rb) (c) TC = a/2Rb (d) TC = a/27Rb

Answer: (a). At the critical point of the van der Waals gas: VC = 3b, PC = (a)/(27b²). (PCVC)/(RTC) = 3/8 ⇒ TC = (8PCVC)/(3R) = 8/3R·(a)/(27b²)·3b TC = (8a)/(27Rb) So the answer is (a).

The value of critical temperature in terms of van der Waals' constant… | NEET 1996 (AIPMT)

Q25NEET 1996 · AIPMTMedium

Mean Free Path & Real Gases

The value of critical temperature in terms of van der Waals' constant $a$ and $b$ is given by

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Answer: (a)

At the critical point of the van der Waals gas: $V_C = 3b$ , $P_C = \dfrac{a}{27b^2}$ .
$\dfrac{P_CV_C}{RT_C} = \dfrac{3}{8} \Rightarrow T_C = \dfrac{8P_CV_C}{3R} = \dfrac{8}{3R}\cdot\dfrac{a}{27b^2}\cdot3b$
$T_C = \dfrac{8a}{27Rb}$
So the answer is (a).

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