Which of the following represents the compressibility factor $Z$ for a real gas at very high pressure, where the excluded volume $b$ is significant?

Solution

1. The van der Waals equation is $(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$.
2. At high pressure, $P$ is very large, so $P+\frac{a{n}^2}{V^2}\approx P$.
3. The equation simplifies to $P(V-nb)=RT$ for 1 mole.
4. $PV-Pb=RT$, which implies $PV/RT=1+Pb/RT$.
5. Hence the answer is (B).