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If Z is a compressibility factor, van de...

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
For 1 mole of a real gas, van der Waals equation is
`(P+(a)/(V^(2)))(V-b)=RT`
At low pressure, V is large and therefore, b can be neglected in comparison to V so that `V-b~-V`. Hence,
`(P+(a)/(V^(2)))V=RT`
or `PV+(a)/(V)=RT" or " PV=RT-(a)/(V)`
or `(PV)/(RT)=1-(a)/(VRT)" or " Z=1-(a)/(VRT)`
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