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Work Air Conditioner Must Do To Keep Room Constant Temperature

  1. Dec 13, 2011 #1
    1. The problem statement, all variables and given/known data
    If a room is at 27C and the surroundings at 42C, and the heat into the room is 2,000 Cal s-1. What is the minimum work the air conditioner must do to keep the room at 27C?


    2. Relevant equations
    COP = Tc/(Th-Tc)
    Win = Qout/(1+COP)

    3. The attempt at a solution
    COP = (300.15/(315.15-300.15)
    COP = 20.01

    Win = 2,000 Cal s-1/(1+20.11)

    W=95.15 Cal s-1 or 398.1 J s-1
    Look okay?
     
    Last edited: Dec 13, 2011
  2. jcsd
  3. Dec 13, 2011 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    You may want to check your expression for W. For a refrigerator output is the heat flow transferred from the cold reservoir, Qc, so COP = output/input = Qc/W. Also, use 0C = 273K.

    AM
     
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