Newton's Law of Heating and Cooling

Background

What happens when you put a roast in an oven? Or take a cold drink out of the refrigerator? Conversely, what happens when you take a pot of soup off the stove? In each case, the object will heat up or cool down until its temperature is the same as its surroundings. How quickly that happens is determined by Newton's Law of Heating and Cooling. The goal of this project is to rediscover this law.

Data

The data for this project will be collected using a thermometer connected to your calculator. First warm up the thermometer by placing it under your arm. Then dunk it in a glass of cold water, and measure the dropping temperatures. For a second set of data, warm the thermometer again, and record the rising temperatures.

Problems

1. Plot the two data sets. Describe the graphs. What kind of function do you think will be a good model for the data? Why?

2. We will fit an exponential model to each function. As usual, we will do this by looking at the log plots. Do we need to do any transformations on the data before graphing the log plots? If so, what?

3. After performing any necessary transformations, graph the log plots of the two data sets and use these to find exponential models for the data. How well do your models fit the data?

4. Using the results of your analysis, state a version of Newton's Law of Heating and Cooling.

You may do this project as a group of up to 4 people, and turn in one report for the entire group. Each member of the group will receive the same grade.

Graded out of 35 points