For a van der Waal's gas $V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}$
$T_{c} = \frac{8_{a}}{27 b R}$ . Numerically the compressibility factor of a van der Waals gas at the critical points is:

0.375

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0.952

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0.567

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Solution

The correct option is A $0.375$
Given, for a van der Waal's gas $V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}, T_{c} = \frac{8 a}{27 b R} .$ Numerically the compressibility factor of a van der Waals gas at the critical point is
$Z = \frac{P_{c} V_{c}}{R T_{c}} Z = \frac{\frac{a}{27 b^{2}} \times 3 b}{R \times \frac{8 a}{27 b R}} = \frac{3}{8} = 0.375$

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V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}

T_{c} = \frac{8_{a}}{27 b R}

V_{c} = 3 b, P_{c} = a / 27 b^{2}, T_{c} = 8 a / 27 b R

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The compressibility factor for a van der Waal’s gas at the critical point is:

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