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Three step gas cycle

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data
    A monatomic ideal gas has pressure p_1 and temperature T_1. It is contained in a cylinder of volume V_1 with a movable piston, so that it can do work on the outside world.

    Consider the following three-step transformation of the gas:

    1. The gas is heated at constant volume until the pressure reaches Ap_1 (where A >1).
    2. The gas is then expanded at constant temperature until the pressure returns to p_1.
    3. The gas is then cooled at constant pressure until the volume has returned to V_1.

    It may be helpful to sketch this process on the pV plane.

    Part 1-
    How much heat DeltaQ_1 is added to the gas during step 1 of the process?
    Express the heat added in terms of p_1, V_1, and A.

    Part 2-
    How much work W_2 is done by the gas during step 2?
    Express the work done in terms of p_1, V_1, and A.

    Part 3-
    How much work W_3 is done by the gas during step 3?
    If you've drawn a graph of the process, you won't need to calculate an integral to answer this question.
    Express the work done in terms of p_1, V_1, and A.

    2. Relevant equations

    R = 8.31


    3. The attempt at a solution

    Part 1-
    I tried Q = p_1*V_1*(C_V/R) = 1.5*Ap_1*V_1 but I was told this is the final internal energy, not the change in internal energy. so I worked out that

    Q = [1.5*p_1*V_1*(AT_1-T_1)] / T_1 but the answer does not depend on AT_1 or T_1

    Part 2-
    all I've got so far is
    W = nRT*ln(V_f/V_i) = pV*ln(V_f/V_i)
    but thats about as far as I get.

    Part 3-
    I got Ap_1*V_1 but this is what the value would be if it were coming from V = 0. So I re-arranged pV=nRT to eventually get

    W = p_1[(p_1V_1)/(Ap_1) - V_1]
    but this is also wrong how do I take into account the initial state, wouldn't I just be able to write W = (Ap_1V_1) - V_1 ?
     
    Last edited: Feb 27, 2010
  2. jcsd
  3. Feb 27, 2010 #2
    I think the first step isn't mentioned.
     
  4. Feb 27, 2010 #3
    thanks for point that out!! i fixed it!!! now its a three step cycle.

    But i still dont know how to figure this problem out!


    please help anyone!!!! pleaseeeeeeeeee!!!
     
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