At low pressure the vander waals equation can be written as ( P + V 2 a ) V = RT . The compressibility factor of the gas is

The compressibility factor Z = RT P V . From the given equation P + V 2 a = V RT , we can write P V + V a = RT , or P V = RT − V a . Therefore, Z = RT P V = RT RT − V a = 1 − V RT a .

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At low pressure the vander waals equation can be written as $(P + \frac{a}{V ^{2}}) V = RT$ . The compressibility factor of the gas is

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The compressibility factor $Z = \frac{P V}{RT}$ . From the given equation $P + \frac{a}{V ^{2}} = \frac{RT}{V}$ , we can write $P V + \frac{a}{V} = RT$ , or $P V = RT - \frac{a}{V}$ .

Therefore, $Z = \frac{P V}{RT} = \frac{RT - \frac{a}{V}}{RT} = 1 - \frac{a}{V RT}$ .

Stream:JEESubject:ChemistryTopic:Real GasSubtopic:Vander Waal's Gas Equation

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