# Model of Temperature Variation inside a Building

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.

T(t)

T

0

T(t)

±A

ω

c