1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!!!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Three step gas cycle
  1. A Three-Step Gas Cycle (Replies: 4)

  2. Ideal Gas Cycle (Replies: 3)