The compressibility factor of a real gas at h | vedclass

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(D) For a real gas, the van der Waals equation is $(P + \frac{an^2}{V^2})(V - nb) = nRT$. For $1 \ mol$ of gas, this becomes $(P + \frac{a}{V^2})(V -

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$1+\frac{Pb}{RT}$

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(D) For a real gas, the van der Waals equation is $(P + \frac{an^2}{V^2})(V - nb) = nRT$. For $1 \ mol$ of gas, this becomes $(P + \frac{a}{V^2})(V - b) = RT$. At high pressure, the volume $V$ is small, so the term $\frac{a}{V^2}$ is negligible compared to $P$. The equation simplifies to $P(V - b) = RT$. $PV - Pb = RT$. Dividing by $RT$, we get $\frac{PV}{RT} - \frac{Pb}{RT} = 1$. Since the compressibility factor $Z = \frac{PV}{RT}$, we have $Z - \frac{Pb}{RT} = 1$. Therefore, $Z = 1 + \frac{Pb}{RT}$.

The compressibility factor of a real gas at high pressure is

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