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Homework Help: Efficiency of a cycle from a diagram

  1. Apr 24, 2012 #1


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    Calculate the efficiency of the heat machine that is shown in the figure. Draw the corresponding Carnot cycle diagram in the S-T plane.

    2. Relevant equations
    [itex]\varepsilon = \frac{ \Delta W}{\Delta Q}[/itex].
    [itex]\Delta Q = T \Delta S[/itex]

    3. The attempt at a solution
    My problem lies in evaluating [itex]\Delta Q[/itex] for the process 1 (or from A to B).
    For the process 2, [itex]\Delta Q=T_2(S_2-S_1)[/itex].
    For the process 3, [itex]\Delta Q=0[/itex] because there's no change in entropy.
    But I'm stuck at process 1. My attempt was [itex]\Delta Q=\Delta T \Delta S=(T_2-T_1)(S_2-S_1)[/itex] but I know this doesn't make any sense.
    Using that non sensical result I find [itex]\varepsilon = \frac{1}{T_2-\frac{T_2^2}{T_1}}[/itex] which makes no sense because if [itex]T_1=T_2[/itex] I get an infinite efficiency while I should get 0. A friend of mine reached [itex]\varepsilon =\frac{T_1-T_2}{T_1+T_2}[/itex] but I don't know how he did nor if that's right either.
    Any help is appreciated.

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  3. Apr 24, 2012 #2

    I like Serena

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    Did you consider that ##dQ=TdS##, and that if T changes with S that then ##ΔQ=∫TdS##?
  4. Apr 24, 2012 #3


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    Actually not! haha.
    Now I reach the same answer as my friend. Thank you very much for that. :biggrin:
    Hmm I'll think about the Carnot cycle. If I need help I'll post here.