Change in thermal energy and Temperature problem

[laser123]

Homework Statement

Compute the change in internal energy, ΔU, and the final temperature, Tf, when 1 mole of an ideal, diatomic gas is compressed adiabatically to 89.700% of its initial volume. The starting point is 22.500°C and 16.100 L. (Assume that the vibrational degree of freedom stays inactive during the process.)

Homework Equations

eq. 1. W=NkTln(Vi/Vf)

eq. 2. Δu=Q+W

eq. 3. u=(f/2)NkT

The Attempt at a Solution

Okay since it's adiabatic I made the assumption Δu=w. So i used the abouve equation and solved for w=(6.02)(1.381)ln(16.1/14.447)=267.175 J

So i manipulate eq 3 and get u=(f/2)Nk(Tf-Ti) and (2u)/fNk+Ti=Tf=12.8548+295.65=308.505K. This the computer says is wrong?

Because when i find the change in Temp i plan on using du=(f/2)NkdT for the change in thermal energy

 

[TSny]

eq. 1. W=NkTln(Vi/Vf)

Does this equation hold for an adiabatic process?

when i find the change in Temp i plan on using du=(f/2)NkdT for the change in thermal energy

Sounds good.