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 and other Models

  1. Sep 26, 2013 #1
    Hello,

    In my Differential Equations class we are learning about modelling with first order differential equations. We learned that Newton's Law of Cooling breaks down when the temperature of the object is approaching the temperature of the room its in. You eventually get to a point where you have

    0 = e^x

    or some variation of that, where of course there is no solution. This leads me to a few questions.

    1.) Are there mathematical models that don't break down, i.e maybe they aren't perfect but they are still a good approximation and

    2.) Have we come up with a newer model of cooling that does not break down at the point were the object temperature reaches the ambient temperature?

    Thanks for your time,

    -Lee
     
  2. jcsd
  3. Sep 27, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

  4. Sep 27, 2013 #3
    I was able to understand some of that material. It actually got me more excited about my differential equations course to know that I am working toward such cool stuff as the heat equation.

    It seemed that the convergence toward equilibrium is still a problem in the heat equation but is dealt with by one-parameter semigroups theory? This is way over my head but is that a correct assessment? Thanks for the relpy,

    -Lee
     
  5. Sep 28, 2013 #4

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    They usually don't go into applications in the beginning differential equations class because it takes too much time to properly motivate each problem ... thus they keep it to the mathematics, and just teach the methods.

    You will start using differential equations in your upper level courses, especially physics and engineering.

    If you are a math major they may offer a course on the theory of ordinary differential equations; you may enjoy this; it would be a senior level or beginning graduate level course.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Newton's Law of Cooling and other Models
  1. A cooling planet (Replies: 2)

  2. Newton's 2nd law (Replies: 3)

Loading...