Expanding the van der Waals equation in powers of $P$ gives $Z = 1 + B^{'} P + C^{'} P^{2} + \dots$ . Using $B = b - a / RT$ and $C = b^{2}$ together with $C^{'} = (C - B^{2}) / (RT)^{2}$ , the third coefficient $C^{'}$ at the Boyle temperature is

Answer: B

T_{B}

the second virial coefficient

B

is zero, so

C^{'} = (C - 0) / (R T_{B})^{2} = b^{2} / (R T_{B})^{2}

, a positive quantity. This is why

Z

rises slightly above 1 at the Boyle temperature once the pressure is appreciable.