1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook