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?
I know that:
P1 • V1 / T1 = P2 • V2 / T2
Eth = 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.