Classical gases not necessarily ideal

[Logan Land]

Systems A, B, and C are classical gases (not necessarily ideal), each with the same number of molecules N ( or same number of moles n if you prefer), where N is constant. We can measure pressures and volumes Pa,Va ; Pb,Vb ; and Pc,Vc for each system. When A and B are in thermal equilibrium, our measurements show that their pressure and volumes satisfy:
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?

 

[I like Serena]

Systems A, B, and C are classical gases (not necessarily ideal), each with the same number of molecules N ( or same number of moles n if you prefer), where N is constant. We can measure pressures and volumes Pa,Va ; Pb,Vb ; and Pc,Vc for each system. When A and B are in thermal equilibrium, our measurements show that their pressure and volumes satisfy:
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?

Hi LLand314!

Not quite. Then you would still have an equation with Pa,Va in it.

The "trick" is to "eliminate" Pa,Va.

If you have for instance:
x-y=3
x-z=5
then you can "eliminate" x as follows.

We can rewrite the first equation as x=y+3.
Substitute that in the second equation to get (y+3)-z=5.
And now we have a relation between y and z, without x.

The same thing applies to your equation, where you should try to eliminate PaVa.