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Derive Newton's Law of Cooling

  1. Jun 19, 2015 #1
    1. The problem statement, all variables and given/known data

    Mathematically prove how Newton's Law of Cooling is derived.

    2. Relevant equations
    Newton’s Law of Cooling states that the rate of change of a temperature of an object is directly proportional to the difference between its own temperature and the temperature of its surroundings (Smith, 2010). Therefore, from this information it can be seen that the following relationship can be interpreted.

    dT/dt ∝ T-Ts

    Where T = temperature of the object and t = time.

    3. The attempt at a solution

    not sure how the k comes into it?
     
  2. jcsd
  3. Jun 19, 2015 #2
    What does the term "directly proportional" mean in mathematical terms? That should answer your question.
     
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