Solve Perfect Gas Homework: A to B Volume Ratio

[liambwfc]

Homework Statement

'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, V_bf = 8/7V₀.'

Homework Equations

P₁V₁/T₁=P₂V₂/T₂
P₁V₁=P₂V₂
2V₀-V_af=V_bf

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.

 

[collinsmark]

Hello liambwfc,

Welcome to Physics Forums!

Homework Statement

'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, V_bf = 8/7V₀.'

Homework Equations

P₁V₁/T₁=P₂V₂/T₂
P₁V₁=P₂V₂
2V₀-V_af=V_bf

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.

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 P_a and P_b.

(2) It wouldn't be difficult now to find the relationship between V_bf and V_af. (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 V_bf and V_o.

Fortunately, you know that
V_bf = V_o + something
V_af = V_o - something (as in the same something)