Truck cylinder, ideal gas law problem

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Homework Statement

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?

Homework Equations

PV = nRT
$$\Delta$$ E_th = (5/2)nR$$\Delta$$T

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^{$$\gamma - 1$$}T^-$$\gamma$$ and use the final pressure to find the volume but that didn't seem to work. Is there another way to go about this?

 

[Flip18064]

finally figured it out using the formula:

W = PV^$$\gamma$$(V_f^1-$$\gamma$$ - V_i^1-$$\gamma$$)/(1 - _$$\gamma$$)