Applications of Differential Equations


The rate of change of temperature, T, of an object placed in a constant temperature medium, Tm (such as air, or a large body of water) is proportional to the temperature difference between the object and the medium.

Try writing that as a differential equation:

                dT/dt = k (T – Tm)

Now, let’s look at a specifc problem:

An object which has a temperature of 100C is placed into air at 20C. Its temperature drops to 50C in 10 minutes. Express T(t).

Summarize the known information.