Adiabatic expansion of O2: finding ΔT with given Cp,m

[smithnh]

Homework Statement

A sample of 2.5 mol O2 (Cp,m = 29.355 J K-1 mol-1) is originally confined in 23 dm3 at 270 K and then undergoes adiabatic expansion against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate q, w, ΔU, ΔT, and ΔH. (The final pressure of the gas is not necessarily 600 Torr.)

Homework Equations

Tf=Ti(Vi/Vf)^(1/c); c=Cv,m/R; Cv,m=Cp,m-R

The Attempt at a Solution

I have found q,w, and the change in internal energy, however I am having difficulty finding the temperature change. Why is my approach not working.

Tf=270K*(23 dm^3/ 69 dm^3)^(8.314 J/mol/K /(29.355 J/mol/k- 8.314 J/mol/K)

Is it that the heat capacity at constant volume is not Cp,m-R and if so how do I find it.

 

[yungwun22]

I think you got to find delta T by using W=C(at constant volume) * delta T, where
C(at constant pressure)- C(at constant volume)= nR