1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    η=1-(Tc/Th)=W/Qh
    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Temperature in a Carnot heat engine
  1. Carnot heat engine (Replies: 5)

  2. Carnot Heat Engine (Replies: 2)

Loading...