Adiabatic process thermodynamics help

[uchicago2012]

Homework Statement

An ideal diatomic gas at 75 K is adiabatically compressed to 40% its original volume. What is its final temperature?

Homework Equations

delta U = Q - W
W = the integral of PdV
PV^gamma = constant
U = 5/2nKT = 5/2nRT (diatomic, ideal gas)

The Attempt at a Solution

So I'm having trouble because I don't know the pressure. I'm sure you can solve it without the pressure, but I didn't really see how to. Since it's an adiabatic process, Q= 0 so delta U = -W. I tried to write equations separately for U and W and set them equal to the negative of one another, but that ended badly, since the two equations were almost identical and everything, including my final temperature, divides out. Also, I wasn't sure if I can just solve for the problem using 1 mole as the amount present, but that's what I tried to do.

 

[Stonebridge]

You need the form of the adiabatic equation with T and V in it.
Do you have this in your notes or book?
It is derived by combining the one you mention, pV^γ = constant, with pV/T = constant. [by division of one by the other to eliminate p]

 

[p21bass]

PV^γ = constant

Since you know this equation, you should probably know this one, too:

TV^γ-1 = constant.

And you should know (or at least have in your textbook) the value of γ. Therefore, you can solve this problem fairly easily.