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PbVb-(beta)Pb-(alpha)Vb+(alpha)(beta)-PaVa=0

When A and C are in thermal equilibrium, we find:

PcVc-PaVa-((gamma)PaVa)/Pc=0

where (alpha),(beta), and (gamma) are constants.

Find the equation relating Pb,Vb and Pc,Vc that is satisfied when system B and C are in thermal equilibrium.

Would I just set the equation for AB = AC and move the B and C's to one said and A to the other?