Truck cylinder, ideal gas law problem

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

One cylinder in the diesel engine of a truck has an initial volume of 500 cm^3. Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 450 J of work to rapidly compress the air. What is its final temperature? What is its final volume?

2. Relevant equations

PV = nRT
[tex]\Delta[/tex] Eth = (5/2)nR[tex]\Delta[/tex]T

3. The attempt at a solution

I found the temperature using the second equation to be 1100 C which is right. However i cannot find the final volume for the life of me. I tried P[tex]\gamma - 1[/tex]T-[tex]\gamma[/tex] and use the final pressure to find the volume but that didn't seem to work. Is there another way to go about this?
finally figured it out using the formula:

W = PV[tex]\gamma[/tex](Vf1-[tex]\gamma[/tex] - Vi1-[tex]\gamma[/tex])/(1 - [tex]\gamma[/tex])

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