Consider the following graph of $Z v s \frac{1}{V_{m}}$ drawn at low pressure and inversion temperature, using the viral form of Van der Waal's equation:
$Z = 1 + (b - \frac{a}{R T}) \frac{1}{V_{m}} + \frac{b^{2}}{{V_{m}}^{2}} + . . . .$
Find the critical volume $V_{c} i n c m^{3}$ ?

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Solution

$Z = 1 + (b - \frac{a}{R T}) \frac{1}{V_{m}}$ at low pressure
at inversion temperature $T = \frac{2 a}{R b}$
$∴ Z = 1 + (b - \frac{b}{2}) \frac{1}{V_{m}}$
$m = \frac{b}{2} = \frac{0.01}{0.01} = 1$
$∴ b = 2, V_{c} = 3 b = 6 c m^{3}$

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