Tufts OpenCourseware
Author: Fulcrum Institute Development Team

When Do I Add the Cream? (~2 hrs.)


Imagine this dilemma: You have just made a cup of scalding hot coffee and need to cool it fast. You're about to add cream but wonder, "Should I add the cream right away or should I let the coffee cool for a few minutes before I add it? Which will cool it faster? Will it make any difference?"

A. Explore: Where does the Heat Flow?

Before you think about adding cream, simplify the problem and explore heat and temperature change in just the coffee.  Consider 2 scenarios:

Scenario 1:

Heating CoffeeSuppose that you have two identical pyrex cups of room temperature coffee. One cup contains 50 ml and the other contains 150 ml of coffee. You place them side by side on a heating plate for the same length of time.

Scenario 2:

Coffee CoolsYou have 2 identical pyrex cups, each containing 80 ml of coffee. The coffee in one is 50°C, the second is 80°C. You leave them side by side on the counter for an hour.

For each scenario, sketch how you think the temperature of the 2 cups of coffee will vary with time and note your rationale. What do you think is different about the coffee in the two cups? What is the same?

To help you think about this in more detail, we used temperature probes to collect data. Print out and examine the Go! Temp graphs. Then, for each scenario, analyze the temperature change with time. (You don't need to post this, it's a chance to explore.)

In each graph, compare the curves for the 2 cups of coffee:

  • How does the pattern of temperature change compare? Use the reading Analyzing Temperature Graphs to identify patterns of temperature change.
  • Look along the length of the curves. Observe the change of temperature in equal time intervals, e.g. in the first 2 minutes, the next 2 minutes,...the last 2 minutes. How does the rate of change of temperature (the change of temperature per minute) compare in equal time intervals ?

What about heat?

This week, you turn your attention from temperature to another concept: heat transfer. Where is the heat in each of these scenarios? The answer may be stranger than you think! Here is a paragraph from Conceptual Physics that shows how a physicist describes heat:

"If you touch a hot stove, energy enters your hand because the stove is warmer than your hand. When you touch a piece of ice, energy passes out of your hand and into the colder ice. The direction of spontaneous energy transfer is always from a warmer thing to a neighboring cooler thing. The energy transferred from one thing to another because of a temperature difference between the things is called heat…Heat is energy in transit from a body of higher temperature to one of lower temperature."  - Hewitt, Conceptual Physics

Keeping Hewitt’s description of heat flow in mind, for each scenario, create diagrams showing the coffee cups and their surroundings and use arrows to show where you think heat is being transferred among components of the system (coffee, cups, air, and stove or counter beneath).

What can you deduce from the temperature data about the rate of heat transfer, or "energy in transit"?

B. Predict: How does the temperature change?

Now return to the dilemma about adding cream to your coffee; If you want to cool scalding coffee fast, should you add the cream right away or should you let the coffee cool for a few minutes and then add the cream?

Draw on your experience with hot beverages and your exploration with heat and temperature in Part A to predict which strategy would cool the coffee fastest. Explain your reasoning. In your journal, sketch prediction graphs that show how you think the temperature in each of the two cups of coffee would change over an hour. Put temperature on the vertical axis and time on the horizontal axis. For each cup, be sure to show the starting temperature (the same 80°C in each case), the final temperature, and the general shape of the curve.

NOTE: Using the Predict Tool in Logger Lite - You can also draw a prediction graph in Logger Lite. Click on the New button to open a new blank graph, then click the Predict button. You can draw directly on the graph. To save your prediction, save the file. If you like, you can collect data on top of a prediction drawing.

C. Investigate

Now use your temperature probes to test your prediction. You could use coffee for this investigation, but you'll probably find it easier to use a cup of water as a substitute. Use the Coffee and Cream Investigation Sheet to guide your investigation.

Print out and paste the temperature data and graph you collect in your journal.

What happens to the molecules?

At this point, you might have some questions about the Molecular Workbench models that you've been using. To find out more about the use of simulations and models, read the article Models and Molecular Workbench by Judah Schwartz.

Last week you saw how molecular energy changes as the temperature changes. This week use the Molecular Workbench Heat Transfer Model to help you to understand what happens when a hot object is placed near a colder one and to explain the temperature patterns you see on your graph.  To get use the Molecular Workbench, please go to http://mw.concord.org/modeler/ and download the "Heat and Temperature" Module under "Selected Curriculum Modules" (like the Phet simulations in Session 1, you will need Java to run the Molecular Workbench).

The Molecular Workbench model shows 2 substances that are separated by a thin wall. As you work with it, take notes. Use the following suggestions to guide your exploration:

  • Describe how energy is transferred from one substance to the other at a molecular level.
  • Describe what is not changing and what is changing when equilibrium is reached.
  • Describe the pattern you see in the graph of the average energy per particle of each substance.
  • Compare what happens when the temperature difference between the 2 substances is large and when the temperature difference is small.

Note: What's thermal equilibrium? - Two systems in contact are in thermal equilibrium when no heat flows between them.

D. Reason from Evidence

Compare the temperature data you collected for the 2 cups of coffee at several times, e.g., before the cream is added, when the cream is added, in the two minutes after the cream is added, in the last two minutes of data collection. In your journal, take notes describing what your temperature data depicts in each time interval:

  • How does the pattern of temperature change compare? (Use the reading Analyzing Temperature Graphs to identify the patterns of temperature change.)
  • How does the temperature compare and how does the rate of change of temperature (the change of temperature per minute) compare?
  • In view of your work with Molecular Workbench, describe how you think heat is transferred at the molecular level in the coffee, in the cream, in the air. How does that correspond to changes in the temperature graphs?

Finally, consider the description of Temperature and Heat in pages 290 - 294 in Conceptual Physics (tenth edition). As you read, jot down thoughts and questions in your journal. How do these ideas relate to your investigation? What new questions does the reading raise?

To bring together your understanding about heat, temperature, and thermal equilibrium, tackle this week's Challenge.

E. Report

Report on your investigation.

  • Use your notes from Part ID above to tell the story of your temperature graph from both a macroscopic and particle perspective.
  • How did your predictions and measurements compare? In what ways, if any, have your ideas about heat and temperature changed?
  • What advice would you give someone who asks you what's the best time to add the cream and how would you explain your reasoning?