Ideal diatomic gas undergoing adiabatic compression

[hvthvt]

Homework Statement

A very simple question, but I can't figure it out.
An ideal diatomic gas, with rotation but no oscillation, undergoes an adiabatic compression. Its initial pressure and volume are 1.20 atm and 0.200 m^3. Its final pressure is 3.60 atm. How much work is done by the gas?

Homework Equations

Adiabatic, so Q=0 and ΔEint=W (because it is compression right?)
ΔU=nCvΔT

The Attempt at a Solution

Initial pressure = 1.22 * 10^5 pa
Final pressure = 3.66 * 10^ 5 Pa
V = 0.200 m^3

I tried to solve ΔU=5/2*(P2V2-P1V1) but I do not know V1..

Also U=-∫pdV right.. I am messing up, though its pretty simple I guess.
Can anybody help me out please?

 

[Chestermiller]

You need to use the differential form of the equations:

dU=nC_vdT=-PdV

You then need to substitute the ideal gas law into the right hand side of this equation, and then figure out how to integrate it. This might all be worked out in your textbook.

Chet