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Newtons Law of Cooling

  1. Dec 9, 2006 #1
    I have a problem where I have an air cooled condensing unit located in a large room within a building. The volume of the room is approximately 27,195 cubic feet. The air cooled condensing unit rejects 102,600 btu/hr to the space. Assuming the ambient air temperature of the space is 95 degrees fahrenheit, how can I calculate how long will it take to heat the volume of air 1 degree fahrenheit? Any help is appreciated. Thanks.
     
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  3. Dec 9, 2006 #2

    OlderDan

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  4. Dec 10, 2006 #3
    If I am correct:

    Q = Cp(T2-T1) and
    P = QVp/time

    Cp = specific heat and
    p = density
    P = power
    V =Volume
    T2 = final temp
    T1 = initial temp
     
  5. Dec 10, 2006 #4

    OlderDan

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    The mass (Vρ) belongs in your first equation; Q depends on how much air is being heated. It does not belong in the second equation since it is already included in Q.
     
  6. Dec 10, 2006 #5
    I first solve for Q. After I know Q, I can solve for time since I know the power is 102,600 btu per hour. I used SI units and came up with the following:

    Cp = 1,006 J per KgK
    p = 1.15 Kg per cubic meter
    V = 481 cubic meters
    T1 = 308.15K (95F)
    T2 = 310.9K (100F)
    P = 30,060W (102,600 btu per hour

    I wind up with time = 50 sec. I thought it would take longer. Interesting.
     
  7. Dec 11, 2006 #6

    OlderDan

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    I did not check all your conversions, but the volume looks a bit small to me. 1 meter is less than 3⅓ feet, and (3⅓ feet)³ is around 37. 27,195 ft³ should be around 740 m³
     
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