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A real gas obeys the equation of state p...

A real gas obeys the equation of state `p(V-nb)=nRT` where b is van der Waals constant and R is the gas constant. If the pressure and temperature are such that the molar volume of the gas is 10b, what is the value of compressibility factor?

A

`10"/"9`

B

`8"/"9`

C

`12"/"11`

D

`10"/"11`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `p(V-nb)= nRT implies p(V_(m)-b)= RT" "` (where `V_(m)= V"/"n`)
The compressibility factor is given by `Z= (pV_m)/(RT)= 1+(pb)/(RT)`
Suppose pressure and temperature are p. and T. when its molar volume is 10b, then
`p.(V_(m)-b)= RT. implies (p.)/(RT.)= (1)/(10b-b)= (1)/(9b)" or "Z= 1+(p.b)/(RT.)= 1+(1)/(9)= (10)/(9)`.
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