Newton's Model of Cooling

When a hot object, like a cup of coffee, is placed in a cooler environment its temperature drops. The same thing happens to a person outside on a cold day. We know from personal experience that windy days feel colder than calm days. In fact, during winter weather reports often include the "wind chill factor" in addition to the temperature. In this module we study cooling and the effect that wind has on cooling. We begin with an experiment like the one shown below. We heat a cup of water to boiling and then record its temperature as it cools.

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Very roughly a graph of the cooling water will look something like the graph below.

Notice that in this particular graph --

The initial temperature is about 190 degrees Fahrenheit.
The water cools to room temperature in about 30 minutes.
It takes the same amount of time to cool from 190 degrees to 150 degrees as it does to cool from 150 degrees to 110 degrees.
The water temperature appears to drop steadily to room temperature and then stop dropping.

Before looking at actual data what do you think a graph of actual data will look like?

Will the water cool faster when it is hot or when it is merely warm? Or will it cool steadily?
Will the temperature of the water drop to room temperature and then stop dropping?
How long will it take the water to cool?

Before going on sketch a graph showing the way that you think the water will cool.

After we look at this simple experiment we will look at an experiment designed to help us understand the wind chill factor. We will heat two cups of water close to boiling. Then we will place one underneath a fan and leave the other one in calm air as shown in the picture below. As the two cups of water cool we will record their temperature.

missing picture

What do you think data from this experiment will look like?

Will the water under the fan cool faster than the water in calm air?
Will the temperature of the water under the fan eventually drop lower than the room temperature?

Before going on sketch two graphs comparing what you think will happen as the two cups of water cool. Be sure to think about your expectations and to draw the graphs described above before going on.

Ideally you should work through this module using data that you collect. Click on the button below for instructions about collecting your own data using the Texas Instruments CBL.

Click on the button below to continue using either your own data or data provided in these files.

Copyright c 1995 by PWS Publishing Company, a division of International Thomson Publishing Inc. Comments to Frank Wattenberg, Department of Mathematics, Carroll College, Helena, MT 59625.