As I was reading Stephen Hawking's "The Universe in a Nutshell," I came across a discussion of Strominger and Vafa's p-brane model of black holes. Hawking describes that for certain classes of black holes, the p-brane model predicts that information that falls into the black holes will be...
Using the taylor series result
Vm / Vm - b = 1 + b / Vm + ...
and the definition of hte compressibility factor Z = PVm / RT, derive an expression for the first virial coefficient in terms of a and b for the Berthelot equation of state.