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Thermodynamics closed cycle entropy cycle

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    The figure below shows a plot of temperature T versus entropy S for the closed cycle of a particular heat engine (not necessarily an ideal gas) which consists of 3 processes and which operates between two heater reservoirs, a hot reservoir with temperature T1 and a cold reservoir with temperature T2. Assume that each of the 3 processes is reversible.

    A B

    C

    it's a triangle like that with T in the y direction and entropy in the x direction.

    a) show that the heat Q1 absorbed by the engine in the process a to b and the heat Q2 rejected by the engine in process b to c are given by

    Q1 = T1(S2 - S1) and Q2 = (S2 - S1)((T1+T2)/2)

    b) calculate the work Wby performed by the engine in one complete cycle in terms of T1, T2, S1, and S2.

    c) use the def of the efficiency eta = Wby/Q1 to show that

    eta= (T1-T2)/2T1

    2. Relevant equations



    3. The attempt at a solution

    ΔS = ∫dQ/T1 because from a to b it's constant temp

    so pretty simple to get Q1

    I'm not sure how Q2 arises especially that it is (T1+T2)/2

    ΔS = ∫dQ/T = ∫cvndT/T but that wouldn't give me the right answer unless there is some algebra involved

    any help will be appreciated thanks
     
  2. jcsd
  3. Oct 17, 2011 #2
    Is ther a different equation for a system in contact with both reservoirs?
     
  4. Oct 18, 2011 #3
    can anyone give me an idea, i'm still having problems with the Q2 = (S2-S1)((T1+T2)/2)
     
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