Any of the real gas equations of state can be written as a power series expansion. For the van der Waals
equation, we have
= 1 +
At the Boyle temperature TBoyle intermolecular attractive
and repulsive effects are balanced so that the terms linear in P (or 1/V) in the expansion to go to zero.
The Boyle temperature for the van der Waals gas is then
Inspection of the power series expansion for the Dieterici gas shows that
For most gases, experiment shows that the ratio of the Boyle temperature to the critical
temperature is consistently about 2.75 (except for He).