The compressibility factor for a van der Waal | vedclass

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(B) For $1 \ mol$ of a van der Waal gas,the equation is $(P+\frac{a}{V^2})(V-b)=RT$. At high pressure,the term $\frac{a}{V^2}$ is negligible compared

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

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(B) For $1 \ mol$ of a van der Waal gas,the equation is $(P+\frac{a}{V^2})(V-b)=RT$. At high pressure,the term $\frac{a}{V^2}$ is negligible compared to $P$,so $P+\frac{a}{V^2} \approx P$. Substituting this into the equation,we get $P(V-b)=RT$. Expanding this gives $PV-Pb=RT$,which rearranges to $PV=RT+Pb$. The compressibility factor $z$ is defined as $z=\frac{PV}{RT}$. Dividing the equation $PV=RT+Pb$ by $RT$,we get $z=\frac{RT}{RT}+\frac{Pb}{RT}$. Therefore,$z=1+\frac{Pb}{RT}$.

The compressibility factor for a van der Waal gas at high pressure is

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