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For a van der Waal's gas with a = 0.2463 atm ${lit}^{2} {mol}^{- 1}$ b = 0.01 lit ${mol}^{- 1}$ subjected to adiabatic free expansion at an initial temperature of 650 K will show which of the following characteristics?

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$q = 0, w = 0, Δ T = 0$

$q = 0, w = 0, Δ T > 0$

$q = 0, w = 0, Δ T < 0$

$q \neq 0, w = 0, Δ T = 0$

answer is B.

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Detailed Solution

$T_{i} = \frac{2 a}{b R} = \frac{2 \times 0.2463}{0.01 \times 0.0821} = 6000 K$

Above inversion temperature on adiabatic free expansion temperature of gas will increase.

$\begin{array}{l} P_{ext} = 0; w = 0; q = 0 (adiabatic); Δ U = 0 \\ T_{f} = T_{i} + \frac{1}{n C_{v}} [n^{2} a (\frac{1}{V_{2}} - \frac{1}{V_{1}})] \end{array}$

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