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Calculating reversible adiabatic expansion

  1. Sep 16, 2015 #1
    I have some homework that I am just not able to figure out.

    There is a 2kg parcel of air at T1=32°C and p1= 0.8 atm
    This parcel of air expands untill it is at T2=12°C

    Also, during the expansion 3.2 g of water will condense due to the dT (ΔvapH (water) = 40.65kJ mol-1

    Also: Cv=0.718 kJ kg-1K-1


    I understand that dU+dW=dQ=0
    and that W=-pdV and w=CvΔT

    The steps should be calculating the expansion work, then subtracting the heat from condensation to figure out the work, but I just keep drawing blanks. Can anybody help me? I am not looking for an answer, but mainly the steps to calculate it.
     
  2. jcsd
  3. Sep 16, 2015 #2
    It isn't clear exactly what you are being asked to calculate. Please clarify.

    Chet
     
  4. Sep 17, 2015 #3
    Sorry, I believe I misunderstood the template being that this is my first time here. I hope that the following is more clear.
    1. The problem statement, all variables and given/known data
    Calculate the expansion work done by a reversibly adiabatic balloon.
    Mass air parcel: 2 kg
    T1=32°C = 305K
    p1= 0.8 atm = 81060 Pa
    T2= 12°C = 285K
    Cv= 0.718 kJ kg-1K-1

    Also, during expansion 3.2g water vapor will condense due to the falling temperature.
    The vaporization energy of water is ΔvapH(water) = 40.65kJ mole-1

    2. Relevant equations
    dU+dW=dQ=0
    W=-pdV
    W=CvΔT

    3. The attempt at a solution
    I have made multiple attempts, but so far none have been successful. I think this is mostly because I am not sure what steps to use.
     
  5. Sep 17, 2015 #4
    Your relevant equations suggest that you kind-of have the right idea. Irrespective of whether the process is reversible, if Q = 0, you must have that ΔU=-W. (Your equation for dW = -pdV is incorrect. It should be dW = +pdV).

    The question is, "do you have enough information in the problem statement to calculate ΔU?" You certainly have enough information to get the change in internal energy of the air. What is that equal to? In the case of the water, it isn't clear. In my judgement, you need to know how much water vapor was initially in the balloon. If, in the initial state, the water vapor partial pressure were equal to its equilibrium saturation vapor pressure, how much water would there have been in the balloon?

    Chet
     
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