Question

Show that at high pressures, the compressibility factor z is greater than 1 and at low pressures, z is less than unity.

Answer 1

The compressibility of a real gas is given by,

$Z= 1+\frac{PB}{RT}-\frac{a}{VRT}$

At high T, value of a/VRT decreases

Also at high T, P is high due to which $\frac{PB}{RT}$ increases.

The increase in the second compensates the decrease in the first due to which net value of Z>1 .