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Energy and Entropy from P-V Diagram

  1. Mar 1, 2012 #1
    1. The problem statement, all variables and given/known data
    An ideal monatomic gas is taken through the above cycle where p1= 2 X 105 Pa and V1 = 5 cm3. During the cycle both the pressure and volume will change such that p2 = 2 p1 and V2 = 4 V1.

    a) How much work is done by the gas in going from state a to state c along path abc?
    Wabc = 3 J

    b) What is the change in internal energy in going from b to c?
    Ubc= J

    c) What is the change in internal energy during the complete cycle?
    UTOT = 0 J

    d) What is the change in entropy per mole of gas in going from b to c?
    ΔSbc = J/K

    e) What is the change in entropy per mole during the complete cycle?
    ΔSTOT= 0 J/K

    I am having problems with Parts B and D.

    2. Relevant equations
    Q = nCvdt

    3. The attempt at a solution

    I only have P and V. I cannot use the Ideal Gas Law to calculate n or T because I have two unknowns. I cannot use my Heat Equations because I am still missing n and T. I'm just stuck. If I can calculate B, I think I can get D...I just don't see any way to calculate the Heat in part B. HELP!


    Attached Files:

  2. jcsd
  3. Mar 1, 2012 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Use: ΔU = nCvΔT = n(3R/2)ΔT

    Since PV = nRT, you can express ΔT in terms of ΔP and V (V is constant).

    Use: dS = dQ/T. What is the heat flow in terms of dT and Cv? Integrate that to get ΔS.

  4. Mar 1, 2012 #3
    I can't believe I didn't see that. Once I read "express ΔT in terms of ΔP and V" it all fell together. It took me less than 2 minutes to solve the problems. Thanks! :)
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