Boyle temperature is the temperature at which a non ideal gas behaves most like an ideal gas. At Boyle temperature, set the compressibility factor
Where a and b are van der Waals parameters.
This is the virial equation of state and describes a real gas. The Boyle temperature is formally defined as the temperature for which the second virial coefficient,
In any case, when the pressures are low, the second virial coefficient will be the only relevant one because the remaining concern terms of higher order on the pressure. We then have
where