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Compressibility Factor

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Question

Find compressibility factor(z) for the following equation of state.
$P V = R T - \frac{A}{V} + \frac{2 B}{V^{2}}$
where A and B are constant, p = pressure and V = molar volume.
Write 6*Z in the blank.

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Solution

The equation of state is
$P V = R T - \frac{A}{V} + \frac{2 B}{V^{2}}$ ....(1)
The expression for the compressibility factor is
$Z = \frac{P V}{R T}$
To otain the value of Z, divide equation (1) by RT.
$Z = \frac{P V}{R T} = 1 - \frac{A}{R T V} + \frac{2 B}{R T V^{2}}$
It can also be written as
$Z = \frac{P V}{R T} = 1 - \frac{1}{V} [\frac{A}{R T} + \frac{2 B}{R T V}$

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