Model of Temperature Variation inside a Building

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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.

Contributed by: Enrique Zeleny (January 2013)
Open content licensed under CC BY-NC-SA



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.

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