NEWTON’S LAW OF COOLING

Knight Foundation Summer Institute

Elizabeth Chesick, Haverford College

Introduction:

This lesson is a neat way not only to demonstrate Newton’s Law of Cooling but also to answer a question that people encounter everyday. Suppose you are served hot coffee in a restaurant. You wish to drink the coffee about 15 minutes after it is brought from the coffee pot (after you finish your fast food hamburger). You like to add cream to your coffee, but you still want the coffee to be as hot as possible after those fifteen minutes. Therefore, should you add the cream when the waitress brings the coffee or after about 12 minutes? Remember, the coffee should be as hot as possible.

The important concept here that needs to be considered here is how fast does something cool off, or how fast does the temperature change? What are the crucial factors that affect the rate of cooling? This question also concerned Newton. There is a law – Newton’s law of cooling – that treats this phenomenon. Newton’s Law says that the time a substance takes to cool off depends on the temperature difference between the substance and the surroundings. This law may be written as

time to cool a DT

(or the time to cool is proportional to the temperature difference between hot liquid and surroundings.) Discuss what this means to students. Then have them write a hypothesis for the answer to the question posed above.

Objectives:

1. To determine whether we should add the room temperature cream after 2 minutes or after 12 minutes if we wish to drink the coffee as hot as possible about 15 minutes after it is poured. (If the coffee is allowed to sit for half an hour, it will likely be room temperature, so either case would give the same final temperature after half an hour.)
2. To determine the rate of cooling of the two cases.
3. To develop laboratory techniques useful for chemistry experiments.
4. To develop skills in making graphs.

Vocabulary:

rate

proportional

room temperature

Materials:

per group of 2-3 students:

• 1 hot plate per class
• 2 250 ml beakers
• 2 150 ml beakers
• 2 thermometers
• water
• milk
• instant coffee
• timer
• paper towel
• graph paper
• pencil and paper to record observations

Procedure:

First have the students write down their hypothesis of what they think will happen knowing what Newton's Law states. One partner should do Part A and one partner should do Part B. The parts may be done concurrently.

Part A. Add the milk early

1. Measure 150 ml of water with instant coffee into a 250 ml beaker and heat it on a hot plate until it the temperature reaches 80 degrees.
2. Put 40 ml of milk in a 150 ml beaker.
3. When the coffee has reached 80 degrees, carefully remove it from the hot plate using a paper towel as a pot holder.
4. The temperature of the water may continue to increase a few degrees after it is removed from the heat. When the temperature returns to 80 degrees start taking the temperature every ¸ minute.
5. At the two minute (2 minutes) mark, add the milk and continue taking the temperatures every ¸ minute.
6. Record the temperatures in a chart and keep taking temperatures until the time reaches 15 minutes.
7. Make a graph of temperature versus time, temperature on the y axis and time on the x axis.
8. Compare your graph with your partner. Which slope is steeper? Who has the higher temperature after fifteen minutes. What does this tell you.

Part B. Add the milk later:

1. Measure 150 ml of water with instant coffee into a 250 ml beaker and heat it on a hot plate until the temperature is 80 degrees.
2. Put 40 ml of milk in a 150 ml beaker.
3. When the coffee has reached 80 degrees, carefully remove it from the hot plate using a paper towel as a pot holder.
4. The temperature of the water may continue to increase a few degrees after it is removed from the heat. When the temperature returns to 80 degrees start taking the temperature every 1/2 minute.
5. At the 12 minute mark (12 seconds), add the milk and continue taking the temperature every 1/2 minute.
6. Record the temperatures in a chart and keep taking temperatures until the time had reached 15 minutes. Make both graphs on the same kind of paper with the same numbers on the axes so that they can easily be compared.
7. Make a graph of temperature versus time, temperature on the y axis and times on the x axis.
8. Compare your graph with your partner. Which slope is steeper? Who has the higher temperature after fifteen minutes. What does this tell you.

Data and Results

Record the data in a table such as:

 Time (sec) Temperature A Temperature B 0.0 0.5 1.0 1.5 Etc.

Assessments:

Have the students turn in their hypothesis, data charts, graphs, and conclusion, and possible sources of error (reading the thermometer, adding cream at correct time, graphing, etc) in scientific format.

The results should turn out as follows: The final temperature of the coffee with cream added early (Part A) is a few degrees above the coffee with cream added later (Part B). If the room temperature is 24 or 25 C, there will be little difference. The experiment works best if the temperature of the room is about 20 C, as in the wintertime. Also, the graph for Part A after the cream is added is more horizontal, or has a lower slope, than the graph for Part B until the cream is added. That shows that if the temperature between the liquid (coffee) and the room is greater, the cooling is faster and if the difference in temperatures is less, the cooling is slower. Or, the rate is greater is the temperature difference is greater. As was mentioned before,

Time to cool a DT (Newton’s Law of Cooling).

So, add the cream in the beginning to enjoy your coffee as hot as possible after fifteen minutes.

Conclusion:

Newton’s Law of Cooling may be verified by this experiment.

Errors:

There are errors in reading the thermometer and adding the cream at the specific time. Also, it is easy to make mistakes in the graphing.

Extensions:

The result can be applied to discussions involving climate and the cooling or earth and water - cooling of ground in dessert areas, cooling of water in lakes and oceans, and warming of oceans for swimming. In a liquid mixture, the hot liquid is an energy source and the cold liquid is an energy receiver. Heat energy is transferred from the hot to the cold substance.

A class should observe Newton’s Law of Cooling directly several ways; any of these experiments would demonstrate that hotter water cools faster than cooler water.

• They could just heat water, remove it from the hot plate and then record the temperature every minute as it cooled.
• A shorter experiment would be for each group in the class to have the same quantity of water at different temperatures. As a class, set time zero and record the original temperature ant then record the temperature at some set time later, say three minutes. The class could compare the average rate of temperature drop in three minutes for different initial temperatures.
• You could also say that you recorded cooling data and have them graph the data. Here is some data and a computer generated graph.

Philadelphia Science Content Standards #1: Nature of Science

This experiment answers Benchmark 1 for grades 5-8: " Design, modify, and conduct an investigation through testing, reviewing and occasionally discarding ideas, all of which lead to a better understanding of how things work. " This experiment answers Benchmark 3 for grades 5-8: "Collect and summarize data from an experiment and interpret the results in terms of the data."

Philadelphia Science Content Standards #2: Physical Setting

This experiment answers Benchmark 5 for grades 5-8: "Understand heat, light, electricity, and magnetism and how they relate to the transfer and transformation of energy."

Philadelphia Science Content Standards #5: Designed World

This experiment answers Benchmark 5 for grades 5-8: "Distinguish between energy source, energy transfer, and energy receiver, and explain the different ways of distributing energy and the environmental consequences they may cause."

Philadelphia Science Content Standards #6: Bridges to the Mathematical and Technological World

This experiment answers Benchmark 1 for grades 5-8: "Understand that multimedia communication devices as well as writing, drawing, and measuring using correct units are ways to communicate information to others."

This experiment answers Benchmark 3 for grades 5-8: "Understand that technology and mathematics are essential to science for access to outer space and other remote locations, for sample collection and treatment, for measurement, data collection and storage, and for computation and communication of information."

Cross-references:

This lab could fit into many different areas. First, it is a generally great way to practice some basic scientific techniques – measuring liquid, reading a thermometer, marking data tables, and drawing graphs. In addition, it teaches some physical concepts such as heat transfer.