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  4. If Z is a compressibility factor, van der Waals equation at low pressure can be written as

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Q. If Z is a compressibility factor, van der Waals equation at low pressure can be written as

JEE MainJEE Main 2014States of Matter

Solution:

Compressibility factor $( Z )=\frac{ PV }{ RT }$

(For one mole of real gas)

van der Waal equation

$\left( P +\frac{ a }{ V ^{2}}\right)( V - b )= RT$

At low pressure

$V - b \approx V$

$\left( P +\frac{ a }{ V ^{2}}\right) V = RT$

$PV +\frac{ a }{ V }= RT$

$PV = RT -\frac{ a }{ V }$

$\frac{ PV }{ RT }=1-\frac{ a }{ VRT }$

So, $Z=1-\frac{a}{VRT}$