# Ideal gas question

1. May 17, 2012

### liambwfc

1. The problem statement, all variables and given/known data
'A closed cylinder containing a perfect gas at 300K is divided into two parts A and B of equal volume, V0 by a freely moveable close-fitting piston. The gas in B is then heated to 400K but that in A is maintained at 300K. Show that the final volume of the gas in B, Vbf = 8/7V0.'

2. Relevant equations
P1V1/T1=P2V2/T2
P1V1=P2V2
2V0-Vaf=Vbf

3. The attempt at a solution
Not really sure, just continually messing about with the above equations with no substantial progress. Obviously two equations, one for Gas A and Gas B. Would really appreciate any help, thanks.

2. May 17, 2012

### collinsmark

Hello liambwfc,

Welcome to Physics Forums!
You're on the right track with your
P1V1/T1 = P2V2/T2
formula.

Two things:

(1) The problem statement mentioned that the two volumes are separated by "a freely moveable close-fitting piston." That should tell you something about the relationship between Pa and Pb.

(2) It wouldn't be difficult now to find the relationship between Vbf and Vaf. (If you've used hint 1 correctly, it's almost a no-brainer.) But that is not what the problem statement is asking. It's asking for a relationship between Vbf and Vo.

Fortunately, you know that
Vbf = Vo + something
Vaf = Vo - something (as in the same something)