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 + (Pb/RT)
C. Z = 1 + (RT/Pb)
D. Z = 1 − (a/VRT)
[IIT-JEE(Main)-2014]
Van der Waals equation for 1 mole of real gas is-
(P + a/V2) (V − b) = RT
At low pressure, volume is very large and hence correction term 'b' can be neglected in comparison to very large volume of V.
i.e. (V − b) ≈ V
Hence, the above equation becomes-
(P + a/V2) V = RT
PV + a/V = RT
PV = RT − a/V
Dividing both sides by RT, we get-
PV/RT = 1 − (a/VRT)
So, the correct option is D.
