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Homework Help: Temperature in a Carnot heat engine

  1. Apr 16, 2017 #1
    1. The problem statement, all variables and given/known data
    A Carnot heat engine takes 95 cycles to lift a 10 kg. mass a height of 11 m . The engine exhausts 14 J of heat per cycle to a cold reservoir at 0∘C.

    What is the temperature of the hot reservoir?

    2. Relevant equations
    3. The attempt at a solution
    I've tried: (Energy to lift mass)/(number of cycles)=W, so (mgh)/95=((10kg)(9.8m/s^2)(11m))/95= W=11.35 J/cycle
    ∴ 1-(Tc/Th)=11.35/14, so Tc/Th=1-(11.35/14), Th=Tc/(1-(11.35/14))=273 K/(1-(11.35/14))=1440 K=1170°C

    This is an incorrect answer, and logically it seems too high.

    I also considered where the 14 J/cycle exhausted to the cold reservoir is the work out, but then I don't know how to calculate Qh so that I'd only have one variable in the equation listed under 'Relevant Equations'.
  2. jcsd
  3. Apr 16, 2017 #2


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    The problem statement says 14 J is the heat exhausted to the cold reservoir, so it's ##Q_\text{C}##, not ##Q_\text{H}##. You calculated ##W## correctly. How do you get ##Q_\text{H}## from ##Q_\text{C}## and ##W##?
  4. Apr 16, 2017 #3
    Qh=W+Qc=11.35+14=25.35 J/cycle

    Plug that into W/Qh=1-(Tc/Th) and Th=494 K=221°C

    That's the correct answer, thanks so much!!
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