Newton's Law of Cooling

Newton's Law of Cooling states that if a body initially at temperatureis placed in an environment with ambient temperaturethe temperature of the hot body falls at a rate proportional to the temperature difference between it and it's surroundings:

The minus sign indicates thatis decreasing.

This equation can be solved to find the temperature of the hot body as a function of time.

Example: A body with an initial temperatureis placed in an environment with ambient temperatureIf after 1 hour the body has cooled to a temperature offindand the time for the temperature to fall to

The Law of cooling applies equally well if the ambient temperature is higher than the initial temperature of the body,. In this case we obtain