Comparing the two forms of the virial equation, $Z = 1 + B / V_{m} + C / V_{m}^{2}$ and $Z = 1 + B^{'} P + C^{'} P^{2}$ , which of the following are correct?

Answer: A, B, C

Substituting

P = \frac{RT}{V _{m}} (1 + \frac{B}{V _{m}} + \dots)

into the pressure series and matching powers of

1/ V_{m}

gives

B^{'} = B / RT

and

C^{'} = (C - B^{2}) / (RT)^{2}

(A and B true). Since

B^{'} \propto B

, both are zero at the Boyle temperature (C true).

C^{'}

can be negative when

B^{2}

exceeds

C

, which happens for many gases at low temperature (D false).