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If Z is the compressibility factor, van ...

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

A

`Z = 1+ ( RT)/( Pb)`

B

`Z = 1- ( a) /( VRT)`

C

`Z = 1- ( Pb)/( RT)`

D

`Z = 1+ ( Pb)/( RT)`

Text Solution

Verified by Experts

The correct Answer is:
B
Compressibility factor ( Z ) = `( PV)/( RT)`
For one mole of a real gas van der Waals equation
`( P + ( a)/( V^(2))) ( V - b) = RT`
At low pressure
`V -b = V ` ( b can be neglected )
`( P + ( a)/( V^(2))) V = RT `
`pV + ( a)/( V ) = RT `
`pV = RT - ( a)/( V )`
`( pV)/( RT) = 1- ( a)/( VRT)`
`:. Z = 1- ( a)/( VRT)`
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