Adiabatic Expansion Homework: q,w,ΔU,ΔT,ΔH

[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

 

[Blueshift5]

Your approach is not working because you are using the wrong formula for calculating the temperature change. The formula you have used is for an isothermal process, where the temperature remains constant. In an adiabatic process, heat is not exchanged with the surroundings, so the temperature change cannot be calculated using this formula.

To find the temperature change in an adiabatic process, you can use the following formula:

Tf = Ti * (Vf/Vi)^((γ-1)/γ)

Where γ is the adiabatic index, which for a diatomic gas like O2 is equal to 1.4.

Using this formula, you should be able to find the temperature change and then calculate ΔH using the formula ΔH = ΔU + PΔV. Remember to convert the pressure from Torr to Pa before using it in the formula.

I hope this helps with your homework. Good luck!