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Carnot Engine - Carnot Refrigerator

  1. Aug 13, 2004 #1
    This is just a common problem solving question, which I cannot make, I suspect because I'm bad at maths. Anyway, I want to see it done, hopefully to grasp it. I am doing physics, so, it's an exercise from one of my books.

    18-11. Show that the efficiency e of a Carnot engine and the perfomance coefficient K of a Carnot refrigerator are erlated by K=(1-e)/e. The engine and the refrigerator operate between the hot and cold reservoirs.

    e= Th-Tc/Th
    K= Tc/Th-Tc
  2. jcsd
  3. Aug 17, 2004 #2
    o.k. I'm going to give it a try.
    e=(Th-Tc)/Th => e= (Th/Th)-(Tc/Th)=1-(Tc/Th) => Tc/Th=1-e
    k=Tc/(Th-Tc) then, dividing the numerator and also the denominator by Th.
    Tc/Th Tc/Th 1-e 1-e 1-e
    k=------------- = ---------- = --------- = ------- = -------
    (Th-Tc)/Th 1-(Tc/Th) 1-(1-e) 1-1+e e
  4. Aug 17, 2004 #3
    well, I was typing in a different way, but it didn't work because my Latex is not good

    k=(Tc/Th)/(1-(Tc/Th)) = (1-e)/(1-1+e) = (1-e)/e
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