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Ideal gas thermodynamics

  1. Apr 2, 2013 #1
    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. jcsd
  3. Apr 2, 2013 #2

    DrClaude

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    Staff: Mentor

    Welcome to PF!

    And what is your question?
     
  4. Apr 2, 2013 #3
    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
     
  5. Apr 3, 2013 #4

    DrClaude

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    Staff: Mentor

    That would be dU.

    Please tell.

    To get dH and dA, you'll have to integrate the equations from the initial conditions to the final conditions.
     
  6. Apr 3, 2013 #5
    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?
     
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