# Thermodynamics problem - adiabatic process

## Homework Statement

One cylinder in the diesel engine of a truck has an initial volume of 600 cm^3. Air is admitted to the cylinder at 35 C and a pressure of 1.0 atm. The piston rod then does 500 J of work to rapidly compress the air. What is the final temperature and volume?
I found the final temperature to be 1000C, but I can't find the final volume

## Homework Equations

PV^y=PV^y
W=deltaE
deltaE=nCv(change in temp)
y=1.4
PV=nRT

## The Attempt at a Solution

I don't know, honestly. It's maddening not to even know what to do or where to start.
Help?
Thank you.

ehild
Homework Helper
Show your work, please. How did you get 1000 °C for the final temperature?

What do you mean on PV^y=PV^y? that pV^y is equivalent to itself? If you use the correct equation for the adiabatic process together with the ideal gas law, you can find the relation between the temperature and volume.

ehild

I meant PV^y stays constant throughout the adiabatic process. I guess it should be P1V1^y=P2V2^y.
What do you mean by the "correct" equation for the adiabatic process?

Also, I know the final temperature is the correct answer, but what I did was:
W=nCv(deltaT)
n=PV/RT
n=(101325)(.0006)/8.31(308)
Cv for air=20.85 (it's in my physics book)
W=500J
500=nCv(Tf-308)
Tf= 1000 C

Hahahaha, WOW. I hate masteringphysics.
I just wiki'd Adiabatic process and found the simple equation
VT$$^{\alpha}$$=Constant
Where $$\alpha$$=5/2 for diatomic gases (like air).
I found V$$_{f}$$ to be 17.3, but that was wrong because my temperatures weren't accurate enough.
Guess what though? Masteringphysics TOLD me to use those values after I entered in more accurate values.
WTF.

ehild
Homework Helper
The temperature is 1010 K, not C°. In what units did you get that 17.3 for the volume? The original volume was 0.0006 m3, and it was compressed, how can it be larger then?

Always write out the units!

ehild

Masteringphysics told me to use 1000C for furture calculations in the problem, hence why it I got it wrong... And 17.3 cm^3, so it's not larger.