Calculate Final volume and temperature of piston

[Jamie_Pi]

Homework Statement

One cylinder in the diesel engine of a truck has an initial volume of 640 cm3. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 500 J of work to rapidly compress the air. What are its final temperature and volume?

Homework Equations

I know that:
P₁ • V₁ / T₁ = P₂ • V₂ / T₂
E_th = W + Q
And I know that work is the integral of pressure in terms of volume, but I'm not sure how to find the final values based on what I'm given.

The Attempt at a Solution

I set up my equation as by converting everything to SI units, so:
P₁ = 101325 Pa
V₁ = 0.64 M³
T₁ = 305.15 K

And I know that I should be able to find the final volume based on the work done, but I don't know how.

 

[Nidum]

What is the difference between an isothermal and an adiabatic compression process ?
Which compression process is used in your engine ?
How can you use this information to solve the problem ?