Newton's Law of Cooling states that if a body initially at temperature
is placed in an environment with ambient temperature
the temperature of the hot body falls at a rate proportional to the temperature difference between it and it's surroundings:
The minus sign indicates that
is 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 temperature
is placed in an environment with ambient temperature
If after 1 hour the body has cooled to a temperature of
find
and the time for the temperature to fall to
is higher than the initial temperature of the body,
. In this case we obtain