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!

Homework Help: Air conditioner homework

  1. Nov 22, 2006 #1
    A home is kept cool by an air conditioner. The outside temperature is 311.75K and the interior of the home is 288.55K. If 127kJ/h of heat is removed from the house, what is the minimum power that must be provided to the air-conditioner? answer in kJ/h
    my work

    COP = Th / (Th - Tc)
    = 311.75 / (311.75 - 288.55)
    = 13.44

    W = 127kJ/h / 13.44
    = 9.45 kJ/h this is incorrect according to the homework server

    Anybody know where i went wrong on this one???
    any help is appreciated!:smile:

  2. jcsd
  3. Nov 23, 2006 #2


    User Avatar
    Science Advisor
    Gold Member

    There's no way the electrical input can be less than the power removed! You need to multiply, not divide.
  4. Nov 23, 2006 #3
    Ok we went about this a different way and got the right answer...for those of you who may have the same problem...

    Th, Tc and Qc are given in the problem...isolate Qh using Qh/Th = Qc/Tc
    to find work
    W = Qh-Qc

    thank you for your help marcusl i realised i was going about it the wrong way :)
  5. Nov 24, 2006 #4


    User Avatar
    Science Advisor
    Homework Helper

    I think that is not true. If the temperature difference goes to zero, it should ideally take no work to move the heat from one resevoir to another. I think the only problem with the original calculation is that the OP was using the COP for heating instead of the COP for cooling.


    Qh/Th = Qc/Tc
    Qh = Qc(Th/Tc)
    W = Qh - Qc = Qc(Th/Tc) - Qc = Qc[(Th/Tc) - 1] = Qc(Th- Tc)/Tc = Qc/COP_cooling

    COP_cooling = Tc/(Th- Tc) = 288.55/(311.75 - 288.55) = 12.44

    W = 127kJ/h/12.44 = 10.21kJ/h
  6. Nov 24, 2006 #5
    ahhh ok i see what i did wrong!

    Perfect thank you very much for your time!!!

    Sergio :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook