# Cooling problem

• Feb 21st 2010, 05:07 PM
calculuskid1
Cooling problem
A thermometer is taken from a room temperature 22degreesC and placed outside where the temperature is -10degreesC. One minute later, the thermometer reads 10degreesC. Use Newton's law of cooling to find the temperature T of the thermometer after t minutes.
• Feb 21st 2010, 05:14 PM
skeeter
Quote:

Originally Posted by calculuskid1
A thermometer is taken from a room temperature 22degreesC and placed outside where the temperature is -10degreesC. One minute later, the thermometer reads 10degreesC. Use Newton's law of cooling to find the temperature T of the thermometer after t minutes.

Newton's law of cooling says that the rate of temperature change of an object is directly proportional to the difference between the object's temperature and the temperature of its environment.

$\displaystyle \frac{dT}{dt} = k[T - (-10)]$

separate variables, integrate, and get temperature, $\displaystyle T$ , as a function of time, $\displaystyle t$ .