Which of the following statements about the virial equation of state are correct?

AThe virial coefficients of a given gas depend only on temperature
BThe second virial coefficient can be related to the pair intermolecular potential
CFor a van der Waals gas the third virial coefficient $C$ is independent of temperature
DThe virial expansion in $1/ V_{m}$ converges for all densities including the liquid

Answer: A, B, C

Virial coefficients are temperature functions characteristic of the gas (A true). Statistical mechanics gives

B (T)

as an integral over the pair potential (B true). For a van der Waals gas

C = b^{2}

, with no

T

dependence (C true). The series is useful only at low and moderate density and does not describe the liquid state (D false).