Volume 6, No. 2, Fall 2002

Contents | PDF Version

Figure 1. A row of nine good conductors with "H" on one end and "C" on the other. Use this to estimate temperatures. The computer simulation shows varying mixes of red and blue for each 10°C step from 0°C to 100°C. As the simulation runs, the temperature of each agent will be graphed in the block beneath it.

Monday's Lesson

Modeling Heat and Temperature

By Bob Tinker

Students (and most adults, too) find questions like these difficult. A Concord Consortium project, Data & Models, is exploring whether one kind of mathematical model can help students understand these concepts, for example, the conduction of heat through different materials. (Read about the tools we are developing to help students understand temperature in the cover story of this issue.)

Early in the project, I made a simple AgentSheets model to help prototype our software. Since this model is easy to share over the Web, we invite you to try it out with your students. In your Web browser, go to:

http://www.concord.org/applets/heat-flow

For this Monday's Lesson we have developed some investigations into heat and temperature that you can use with the AgentSheets model. Because of space limitations we can't provide all of the investigations here. You can find the complete set of activities and more detailed instructions on the Web site.

When you start the simulation, you will see a blank worksheet with seven square blocks across the top, as in the screen shown on the right. These are the "agents" for this model (see the key at the right). The tools for manipulating the agents are arranged vertically along the left side of the worksheet.

You can put any number of agents in the worksheet and move them around with the tools while the model is running. Once you become familiar with the agents in the worksheet, try running some trial simulations to get used to the model. For example, you could try putting a fast (good) conductor next to a hot agent and then moving it away. Put the good conductor next to a cold agent and move it away. Note the change in color. Repeat with a slow (poor) conductor and an insulator.

Now make a horizontal row of nine good conductors and place a graph under each. Put a hot agent at one end and a cold one at the other. In a short time, you will see that the conductors form a color gradient between the hot agent and the cold agent. The steps will be 10°C apart. Predict what will happen if you move the hot agent away from the end of the row. What would happen if you were to substitute a poor conductor for one of the nine good conductors? What if you substituted an insulator for one of the good conductors?

Now investigate the following question:

What happens when you mix things with different temperatures?

First, make a row of nine good conductors with "H" on one end and "C" on the other. Use this to estimate temperatures. The computer simulation shows varying mixes of red and blue for each 10°C step from 0°C to 100°C. As the simulation runs, the temperature of each agent will be graphed in the block beneath it.

Set one good conductor agent at 100°C by touching it to an "H" agent and then removing it. Make a second good conductor agent 0°C by touching it to a "C" agent. "Mix" these two blocks by placing them next to each other. From the resulting color, estimate their final temperature.

Predict what will happen before trying each of the following experiments:

• Mix four hot blocks with one cold one. Use only fast conductors.

• Mix four cold blocks with one hot one. Use only fast conductors.

• Repeat all these experiments with slow conductors and insulators.

• Mix one hot fast conductor with one cold slow conductor.

The Science of Heat and Temperature

The difficulty in understanding these simulations is that the flow of heat is hidden from view. Nevertheless, heat flow plays a critical role in the changes that are taking place. The only way any of the agents changes temperature is when heat flows in or out. The model calculates how much heat energy flows in and out of each agent. Heat always flows from a hot agent to a cold one. The amount of heat that flows depends on the difference in temperature and the thermal resistance of each block. The good conductors have little resistance to the flow of heat, while the insulator has high resistance. In this model, the thermal resistances of the three conductors are in the ratio of 1 to 10 to 500.

The degree of temperature change of a block caused by a certain amount of heat inflow depends
on its heat capacity. Something with a high heat capacity is hard to heat up; it takes a lot of heat to increase its temperature. The agents in the model have heat capacities of 10 (for the fast conductor) to 2 (for the slow conductor) to 1 (for the insulator). This explains why it takes five "slow" blocks to balance the warming or cooling effect of one "fast" agent. Both the heat capacity and thermal resistance determine the thermal properties of any object.

Educational Significance

These simple investigations should help students get a "feel" for heat flow and conduction. You could test this by asking students the questions at the beginning of this article before and after they explore these investigations. We would be most interested in any insights you gain about your students' learning of these ideas.

How hard is it for students to understand all these "hidden" properties: heat flow, thermal resistance, and heat capacity? If these ideas are too abstract for beginning students, does exploring the model provide an alternative? Can they gain sufficient intuition from models like this to answer the questions that begin this article? Will insights from these models help students understand the more abstract ideas? As they say, further research is needed, but it seems likely that experiences of this type could be the foundation for deeper learning.

A deeper question concerns the value of models like this one that do not try to provide mechanistic explanations. An alternative kind of model would show what is happening at the atomic scale. In such a model, heat flow could be visualized as the transfer of random motion from areas where there is a lot of motion to areas with less. But we'll save that for another Monday.

Article Links & Notes

Data & Models - http://www.concord.org/data-models/

AgentSheets - http://www.agentsheets.com

The Data & Models project is funded by National Science Foundation grant #REC99-73179.

The projects described in this newsletter are supported by grants from the National Science Foundation, the U.S. Department of Education, the Noyce Foundation and others. All opinions, findings, and recommendations expressed herein are those of the authors and do not necessarily reflect the views of the funding agencies. Mention of trade names, commercial products or organizations does not imply endorsement.