Math108Project

# Math108Project - Jones 1 Introduction Newtons Law of...

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Jones 1 Introduction Newton’s Law of Cooling is a valuable equation that allows for the calculation of heat loss when an object cools. Newton formulated this law by viewing the changing temperature of a hot object while it cooled (Peterson). Newton’s Law of Cooling is very useful in several situations. It is often used for optimizing the heat loss and gain of insulated building to save on heating and cooling costs. In some cases, insulation has different effects than one might think (Berry & Houston). Newton’s Law of Cooling can help asses the heat loss and help create a more accurate model for energy costs of the house. Newton’s Law of Cooling is often referenced as a useful tool for coroners to predict the time of death of a corpse. They need only know the body’s current temperature and the ambient temperature of the environment to make a good prediction for a time of death. This is not an extremely accurate procedure but can give the coroner a good idea of when the body was last at normal human body temperature, or 98.6 degrees Fahrenheit (Berry & Houston). These are only a couple of examples of Newton’s Law of Cooling, which is obviously a very good and useful model of the way an object lowers its temperature. The Mathematical Model Newton’s Law of Cooling can be stated fairly simply as a differential equation: 0 ) 0 ( ) ) ( ( ) ( ' T T A t T t T = - = Where T (t) is the temperature of a liquid in a container, A is the ambient temperature of the air around the container and T 0 is the initial temperature of the liquid. In my case the equation would be:

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## This note was uploaded on 10/21/2008 for the course MTHSC 108 taught by Professor Any during the Fall '08 term at Clemson.

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Math108Project - Jones 1 Introduction Newtons Law of...

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