Model of Temperature Variation inside a Building

The interior temperature of a building changes with the weather outside. Suppose the initial temperature is and that varies between in Fahrenheit degrees with a frequency . Using Newton’s law of cooling, it is possible to write a differential equation for the temperature as a function of time, measured in days, choosing an initial value . The plot of the solution over a range of temperatures is shown, as well as the direction field. Notice that the temperature tends to stabilize after several days.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The differential equation is ( is a constant)
with the analytical solution
[1] J. R. Brannan and W. E. Boyce, Differential Equations, An Introduction to Modern Methods and Applications, 2nd ed., Hoboken, NJ: John Wiley & Sons, 2011 pp. 11–13.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.