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Differential Equation Problem

  1. Mar 5, 2006 #1
    hi, i am having trouble with this problem...

    An apple cobbler is taken out of the oven at 7:00PM one Saturday night. At that time it is piping hot at 100C. At 7:10PM its temperature is 80C, and at 7:20pm, it is 65C. What is the temperature of the kitchen in which the apple cobbler is being held?
  2. jcsd
  3. Mar 5, 2006 #2


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    What have you tried so far?
  4. Mar 5, 2006 #3
    To solve you may use Newton's law of cooling

    [tex] \int_{T_{0}}^{T} \frac{dT}{T-T_{s}} = - \kappa \int_{t_{0}}^{t} d t^{\prime} [/tex]

    where To is the initial temperature, Ts is the temperature of the environment (which is what we are after), k is a material constant, etc. Integrate both sides of this equation, and solve for T, and use the three boundary conditions to solve. You should get a reasonable answer for the room temperature. hope this helps, sincerely x
  5. Mar 5, 2006 #4
    thank you for that, we recently learned about that in physics but for some reason i couldnt put 2 and 2 together, i was going in a completely different direction.
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