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Thermodynamics - Cycle efficiency

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the following reversible cycle:

    2ceqedh.png

    Where S2=S3=(S1+S4)/2 .
    Prove that the efficiency η is:

    η= 1 - 2*T6 / (T1+T3)


    2. Relevant equations



    3. The attempt at a solution

    I know that in a T-S diagram the heat received by the system is equal to the area delimited by the upper boundaries of the diagram and the line T=0. I also know that the heat dispensed by the system is equal to the area under the diagram (I got the same results calculating both heats analitically). Therefore I get:

    η = 1 - (S4-S1)T6 / [ (S2-S1)T1+(S4-S2)T3 ] =
    = 1 - 2*S2T6 / [ (S2-S1)T1+(S4-S2)T3 ]

    I don't know how to get rid of the entropies tho... If anyone could point me in the right direction I'd appreciate.

    Thanks!
     
  2. jcsd
  3. Nov 23, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    Check the blue highlighted region. I don't believe it's correct. Note that S4-S1 ≠ 2S2

    Also, think about the relation between S2-S1 and S4-S2
     
  4. Nov 23, 2012 #3
    Oh, for some reason I tought S2 was equal to (S4-S1)/2 instead of (S1+S4)/2 ....

    I can solve it from here.
    Thanks!
     
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