# Ideal Gas Equation-Thermodynamics

1. Oct 15, 2009

### MarsVolta

1. The problem statement, all variables and given/known data
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

2. Relevant equations

PV=nrT

3. 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 cant find where to get the 4 from or how to cancel the P's

2. Oct 15, 2009

### gabbagabbahey

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

3. Oct 15, 2009

### Andrew Mason

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