What is the Final Temperature T2 for an Ideal Gas During Reversible Compression?

[MarsVolta]

Homework Statement

An ideal gas originally at temperature T₁ and pressure P₁ is compressed reversibly against a piston to a volume equal to one half its original volume. The temperature of the gas is varied during the compression so that at each instant the relation P=AV is satisfied, A=Constant.
Find the final tempertature T₂ in terms of T₁

Homework Equations

PV=nrT

The Attempt at a Solution

P₁V₁=nRT₁
P₂V₁/2=nRT₂

V₁=nRT₁/P₁=2nRT₂/P₂

Canceling yields: P₂T₁=2T₂P₁

Then: T₂=T₁P₂/2P₁

This is where I get stuck..The answer is suppose to be T₂=T₁/4

I can't find where to get the 4 from or how to cancel the P's

 

[gabbagabbahey]

Then: T₂=T₁P₂/2P₁

This is where I get stuck..The answer is suppose to be T₂=T₁/4

I can't find where to get the 4 from or how to cancel the P's

From here, use the information you are given that P=AV...

 

[Andrew Mason]

This is where I get stuck..The answer is suppose to be T₂=T₁/4

I can't find where to get the 4 from or how to cancel the P's

Write the expression for T in terms of V (hint you have to use the relationship between P and V that you are given).

To find Tf substitute .5Vi for Vf.

AM