NEWTONS LAW OF COOLING
Knight Foundation Summer Institute
Elizabeth Chesick, Haverford College
This lesson is a neat way not only to demonstrate Newtons 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 Newtons law of cooling that treats this phenomenon. Newtons 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.
per group of 2-3 students:
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
Part B. Add the milk later:
Data and Results
Record the data in a table such as:
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 (Newtons Law of Cooling).
So, add the cream in the beginning to enjoy your coffee as hot as possible after fifteen minutes.
Newtons Law of Cooling may be verified by this experiment.
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.
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 Newtons Law of Cooling directly several ways; any of these experiments would demonstrate that hotter water cools faster than cooler water.
Philadelphia Science Content Standards:
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."
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.