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## 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:

P

_{1}• V

_{1}/ T

_{1}= P

_{2}• V

_{2}/ T

_{2}

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:

P

_{1}= 101325 Pa

V

_{1}= 0.64 M

^{3}

T

_{1}= 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.