Compressibility factors

The deviation from ideal behavior of a gas is expressed
in terms of the compressibility factor Z, which is defined as the ratio of the
actual volume to the volume predicted by the ideal gas law.

Z = Actual volume/volume predicted by ideal gas law

=
v/RT/P

= Pv/RT

For an ideal gas Pv = RT

and hence Z = 1 at all temperatures and
pressures.

The experimental P-v-T data is used to prepare the compressibility
chart.

Reduced pressure, PR
= P/P
c,

Reduced temperature, TR = T/Tc

Reduced
volume, v
R = v/vc

Where Pc, Tc and vc denote the
critical pressure, temperature and volume respectively.

These equations state that the
reduced property for a given  state is
the  value  of this property in this state divided by the
value of this same property by at the
critical point.

The striking fact is that when such Z
versus Pr diagrams are prepared for
a  number  of different substances, all of them very
nearly coincide, especially when the substances have simple, essentially
spherical molecules.

We need to know only critical temperature and critical
pressure to use this basic generalized chart.

In general it can be noted that
idealized gas behavior for very low pressures as compared to critical)
regardless of temperature. Furthermore, at high temperatures (greater than
twice Tc), the ideal-gas model can be assumed to good accuracy to pressures
as high as 4-5 times Pc.