Because the virial coefficients depend on the temperature, there may be a temperature
at which Z→1 with zero slope at low pressure or high molar volume (Fig. 1.16).
At this temperature, which is called the Boyle temperature, TB, the properties of the
real gas do coincide with those of a perfect gas as p→0. According to eqn 1.20a, Z has
zero slope as p→0 if B = 0, so we can conclude that B = 0 at the Boyle temperature.
It then follows from eqn 1.18 that pVm ≈ RTB over a more extended range of pressures
than at other temperatures because the first term after 1 (that is, B/Vm) in the
virial equation is zero and C/V 2m
and higher terms are negligibly small. For helium
TB = 22.64 K; for air TB = 346.8 K; more values are given in Table 1.5.