1. Not finding help here? Sign up for a free 30min 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!

Newton's Law of Cooling (diff eq. - seperation of variables)

  1. Apr 6, 2010 #1
    Newton's Law of Cooling (diff eq. -- seperation of variables)

    1. The problem statement, all variables and given/known data

    Fresh coffee sitting in a room cooling...you know the routine.
    Anyhow T(0) = 90degreesCelcius.
    Room temp=25degrees Celcius

    find k.
    Then he asks us to use Euler's method to estimate coffee temp after five mins. (using step size h=1).

    2. Relevant equations

    T(t) satisfies the equation: dT/dt=k(T-Troom).
    we know that at T=65 degrees (for coffee) dT/dt (or the rate of cooling, as the problem states)= 1 degree per minute

    3. The attempt at a solution

    Well thought hey look here the ole plug and chug MAY work, lets see...:
    1=k(65-25) brings k=.025. but then I thought, hey for the crap to cool k needs to be negative (this is the only way the limit as t tends to infinity for e^(kt) to tend to 0). So this can't be the appropriate way of going about this. So, without thinking (again) I integrated to see if that would bring about new light. I got

    T=65e^(kt)+25.

    No real help even if the integration is right because I'm missing a value for t to help me solve for k. So I'm a little stuck here.

    I'm confused even more in that the blank where the answer to the second part goes, the Euler's method answer, has a blank that reads T(10)=____________. But I know (thought) the question asked for T(5). Am I missing somthing here?? Thank you, Ian.
     
  2. jcsd
  3. Apr 6, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Newton's Law of Cooling (diff eq. -- seperation of variables)

    Since the temperature is decreasing 1 degree per minute, that means T' = -1, not +1.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Newton's Law of Cooling (diff eq. - seperation of variables)
Loading...