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Newtons Law of Cooling

  1. Feb 19, 2008 #1
    1. The problem statement, all variables and given/known data
    The equation dQ/dt = k ( T - Troom) is newtons law of cooling. dQ/dT being the rate of heat loss. I want to convert this equation to dT/dt, the rate of temperature decay. How do i go about doing this?


    2. Relevant equations



    3. The attempt at a solution

    Is Q proportional to T? then i can just sub it in for Q and solve for the differential equation?
     
  2. jcsd
  3. Feb 19, 2008 #2

    cepheid

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    Well, Q is not proportional to T. Here's what I did:

    [tex] \frac{dQ(t)}{dt} = k(T(t)-T_0) [/tex]

    [tex] \frac{1}{k}\frac{dQ(t)}{dt} +T_0 = T(t) [/tex]

    [tex] \frac{d}{dt}T(t) = \frac{1}{k}\frac{d^2Q(t)}{dt^2}[/tex]
     
  4. Feb 19, 2008 #3

    cepheid

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    To me, it seems like you need T(t) to solve for Q(t). But if you already had T(t), then you could just get T'(t) by direct computation. You don't have it though...
     
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