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Newton's Law of Cooling problem

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data
    The temperature T of a cup of coffee is a function T(t) where t is the time in minutes. The room temperature is 20 ^\circ Celsius. The rate at which the coffee cools down is proportional to the difference between the temperature of the coffee and the room temperature. Use this information to write a differential equation describing the derivative of the coffee temperature in terms of T and t. Use C as your proportionality constant. C should be a positive number. Write T instead of T(t).


    2. Relevant equations



    3. The attempt at a solution
    I don't know where to start.
     
  2. jcsd
  3. Apr 8, 2009 #2
    Re: Derivatives

    I'm pretty sure this is Newton's Law of Cooling. The problem states that the change in temperature(derivative) is proportional(C) to the difference between the two temps(TempCoffee-20).

    So the equation would look like Change in Temp=(Proportional Constant)X(Difference in temperature).

    From there, you get your DT and T to the same side and integrate. The solution involves ln and e. Good luck!
     
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