# Ideal gas thermodynamics

1. Apr 2, 2013

### oxman

1. The problem statement, all variables and given/known data
Two ideal gases are separated by a partition which does not allow molecules to pass from one volume to the other. Gas 1 has: N1, V1, T1, Cv1 for the number of molecules, volume it occupies, temperature in kelvin, and specific heat per molecule at constant volume respectively. Gas 2 has: N2, V2, T2, Cv2. The two gases are in thermal contact and reach a final temperature

a) find the final temperature and the total change in energy of the combined system. Check your answer for the final temperature when N1=N2, V1=V2. Cv1=Cv2

b)Evaluate the total change ina quantity H whose differential change is dH=dU+Vdp for each component and for the entire system

c)evaluate the total change in a quantity A whose differential change is dA=(dU+pdV)/T for each component and for the entire system

2. Relevant equations

U=NVCvdT

3. The attempt at a solution

I already solved for the final temperature for part a, and when evaluated at equal N and V i got Tf=(T2+T1)/2

Last edited: Apr 2, 2013
2. Apr 2, 2013

### Staff: Mentor

Welcome to PF!

And what is your question?

3. Apr 2, 2013

### oxman

i have no idea what is meant by parts b and c

i understand that U=NCvdT

so N1Cv1(Tf-T1)=-N2Cv2(Tf-T2)

and i think i understand how to solve for the total change in energy

4. Apr 3, 2013

### Staff: Mentor

That would be dU.

To get dH and dA, you'll have to integrate the equations from the initial conditions to the final conditions.

5. Apr 3, 2013

### oxman

solving for Tf i get, Tf= ((N1Cv1T1+N2Cv2T2)/(N1Cv1+N2Cv2))

from there i solved for dU1 and dU2 where dU1=N1Cv1(Tf-T1) dU2=N2Cv2(Tf-T2)

i then added them together to get total change in energy

for dA i solved for dA1 and dA2 integrated them and then added them together

essentially for A i got

A=c1ln(Tf/T1) + c2ln(Tf/T2) where c1=N1Cv1 c2=N2Cv2

pdV goes to 0 because there is no change in any of the volumes

correct?