A real gas follows the equation P(V-ab)=nRT under all conditions of temperature and pressure. Show that the compressibility factor of this gas is always greater than one.

Explanation

The equation of state for the gas is: `P(V-nb)=nRT`
The compressibility factor of the gas can be expressed as:
`PV-Pnb=nRT or, PV=nRT+Pnb`
or, `(PV)/(nRT)=1+(Pb)/(RT) or, Z=1+(Pb)/(RT)`
As `(Pb)/(RT)` is always positive, the value of Z will always be greater than 1.