Question:
If Z is a compressibility factor, van der Waals equation at low pressure can be written as
If Z is a compressibility factor, van der Waals equation at low pressure can be written as
Updated On: Sep 27, 2024
- $Z=1+\frac{RT}{pb}$
- $Z=1-\frac{a}{VRT}$
- $Z=1-\frac{Pb}{RT}$
- $Z=1+\frac{Pb}{RT}$
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The Correct Option is B
Solution and Explanation
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, $Z=1-\frac{a}{VRT}$
(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, $Z=1-\frac{a}{VRT}$
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