At very high pressures,the compressibility fa | vedclass

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Question

(A) For one mole of a real gas,the van der Waals equation is given by: $(P + \frac{a}{V^2})(V - b) = RT$ At very high pressures,the volume $V$ is smal

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

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(A) For one mole of a real gas,the van der Waals equation is given by: $(P + \frac{a}{V^2})(V - b) = RT$ At very high pressures,the volume $V$ is small,so the term $\frac{a}{V^2}$ becomes negligible compared to $P$. Thus,the equation simplifies to: $P(V - b) = RT$ $PV - Pb = RT$ $PV = RT + Pb$ Dividing both sides by $RT$: $\frac{PV}{RT} = 1 + \frac{Pb}{RT}$ Since the compressibility factor $Z = \frac{PV}{RT}$,we get: $Z = 1 + \frac{Pb}{RT}$

At very high pressures,the compressibility factor of one mole of a gas is given by

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