Thermodynamics problem - adiabatic process

[Twoism]

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]

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

 

[Twoism]

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

 

[Twoism]

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]

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

 

[Twoism]

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.