Instructor Information
JCE Classroom Activity: #88
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Cool! Rates of Heating and Cooling
Martin Bartholow Johnson County Community College, Overland Park, KS 66213;
[email protected] In this Activity, students measure the rate of warming for a chilled thermometer bulb held in room temperature air, for a chilled bulb held between two fingers, and for a few milliliters of ice-cold water. Students are familiar with the everyday phenomena of warming, but measurement affords the unexpected result that the process is not linear.
Integrating the Activity into Your Curriculum Measuring temperature change is foundational for other experiments in specific heat, heat of fusion, or melting point depression. Rates of warming and cooling can lead into a kinetic description of heat and matter. A previous JCE article uses the cooling of a CBL temperature probe to demonstrate first-order kinetics (2). Another experiment relates to Newton’s Law of Cooling using a practical example (3).
About the Activity
photo by J. J. Jacobsen and R. J. Wildman
Roemer and Fahrenheit developed temperature scales based on two fixed points in the early 18th century. Shortly thereafter Sir Isaac Newton formulated the Law of Cooling: the time needed to cool a substance by one degree is proportional to the temperature difference between the substance and its surroundings. Everyday items such as hot pizza and a hot car engine obey the same law. The rate of temperature change depends on the difference in temperature between the item and its environment. A subtle implication is that the rate decreases as an item approaches the surrounding temperature. Mathematics of the Law are described in another article (1). To relate changes in energy and temperature, students may find a water analogy useful: on a mountainside where the difference in water level is great, water flows quickly, but across a lake there is little difference in height or flow. When a thermometer and the surroundings are at the same temperature, the movement of energy into the bulb is equal to the movement of energy out.
In Question 1, students predict the appearance of a temperature vs. time graph for a chilled thermometer bulb as it warms. Many will assume that the graph will be linear. Sample data Everyday items such as and graphs are in this issue of JCE Online.W Instructors could also ask students to predict a beverage can be cooling behavior, sketch a possible cooling curve for hot water, and collect cooling data to used to illustrate rates test their prediction. of heating and cooling. Trials 1 and 2 (steps 3 and 4) require data collection until the temperature shows no further change. In testing, trial 1 took 5–6 min to come to a constant temperature; trial 2 took 2–3 min. Times will vary depending on surrounding temperatures. In trial 2, the first few readings are difficult to estimate because the temperature changes rapidly. In trial 3, students stabilize the test tube and thermometer using two clamps, a stand, and a polystyrene block. This helps to reduce fatigue during the 20-min data collection. Different sizes of thermometer bulbs give different rates of warming. Groups could compare data for different bulbs. Digital thermometers or CBL temperature probes may also be used. Water may be blotted from the thermometer bulb if desired, but the procedure works well without this additional step. perforated
Answers to Questions 1. Answers will vary. Students will often suggest a linear slope. Many may predict a plateau at room temperature. 2. The graph should show a rapid temperature change near the freezing point and then a decrease in the rate of warming as the temperature approaches room temperature. 3. Answers will vary. Students can be encouraged to recognize that the rate of temperature change decreases as room temperature is approached. The reason for the plateau at room temperature may be apparent to some students. 4. The graphs will not end at the same temperature because the temperature of the surroundings is different in step 4 compared to steps 3 and 5. 5. The initial slope for trial 2 (step 4) will be greater than the slopes for trial 1 (step 3) and trial 3 (step 5) due to the greater difference between the temperature of the bulb and the temperature of its surroundings. 6. The graph remains flat for a period of time at 0 ⬚C (ice melting), then shows a rapid temperature change (water warms after ice melts), and then a decrease in the rate of warming as the temperature approaches room temperature.
This Classroom Activity may be reproduced for use in the subscriber’s classroom.
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Background
References, Additional Related Activities, and Demonstrations 1. Moore-Russo, Deborah A.; Cortés-Figueroa, José E. Using a CBL Unit, a Temperature Sensor, and a Graphing Calculator To Model the Kinetics of Consecutive First-Order Reactions as Safe In-Class Demonstrations. J. Chem. Educ. 2006, 83, 64–68. 2. Cortés-Figueroa, José E.; Moore-Russo, Deborah A. Promoting Graphical Thinking: Using Temperature and a Graphing Calculator To Teach Kinetics Concepts. J. Chem. Educ. 2004, 81, 69–71. 3. Newton’s Law of Cooling. http://www.haverford.edu/educ/knight-booklet/newtoncool.htm (accessed Jan 2007) JCE Classroom Activities are edited by Erica K. Jacobsen and Julie Cunningham
www.JCE.DivCHED.org •
Vol. 84 No. 3 March 2007 •
Journal of Chemical Education
448A
JCE Classroom Activity: #88
Student Activity
Cool! Rates of Heating and Cooling Temperature is a basic unit of measurement. Changes in temperature frequently occur and can often be qualitatively “felt”. However, for quantitative measurements, a temperature scale is necessary. Galileo trapped air in a tube and used changes in the air’s volume to gauge temperature changes, but did not develop a useful calibrated temperature scale. In 1714 Gabriel Fahrenheit calibrated a thermometer using a saturated brine/ice mixture to set 0 ⬚F and a human’s internal body temperature to mark 100 ⬚F. In 1742 Anders Celsius created a more widely used scale with one hundred divisions from the freezing point of water (defined as 0 ⬚C) to the boiling point of water (100 ⬚C at one atmosphere pressure). The rate at which an object changes temperature and how it does so are important in understanding and measuring the flow of energy into or from an object. For example, when you obtain an ice-cold beverage, practical questions could be: How long does the drink stay cold? How does the temperature of the surroundings affect the beverage and its rate of warming? What other variables affect the rate of warming? In this Activity, you will investigate and graph the warming of a chilled thermometer bulb in different surroundings and the warming of a small amount of ice-cold water. You will need: a container that holds ~500 mL; graduated cylinder or measuring cup; thermometer; stopwatch; graph paper; water; ice; test tube; two clamps and stand; small block of polystyrene. A thermometer with a 1-cm long bulb that can be read quickly to ±0.1 ⬚C works well. __1. Prepare a data table with two columns: Time (s) and Temperature (⬚C). Premark the time using 5-s intervals with the starting time set at 0 s, for ~50 measurements. __2. Using a graduated cylinder or measuring cup, measure ~240 mL (1 cup) of cold water into a 500-mL container. Add enough ice to nearly fill the container. Gently stir the mixture with a thermometer (±0.1 ⬚C) until the thermometer shows no further temperature change. __3. Organize three people for data collection. The roles are: 1) call off 5-s time intervals using a stopwatch, 2) read and call out temperature readings, and 3) record the called-out temperatures on the data table from step 1. For a first trial, your Step 4 (left) and step 5 (right) team will first measure the temperature of the chilled mixture for the data point illustrated. t = 0 s. Then, your team will remove the thermometer from the chilled mixture, and record the temperature change of the thermometer every 5 s as it is held in the room temperature air. Do not hold the thermometer near the bulb, so your fingers do not affect the temperature. Collect data until the thermometer shows no further temperature change. __4. For a second trial, repeat steps 1–3, but this time after you remove the thermometer from the chilled mixture, hold the thermometer bulb between a thumb and forefinger. Predict what will happen to the rate of warming. __5. Mount two clamps on a stand. Place a small block of polystyrene in the upper clamp and a test tube in the lower clamp. Insert the thermometer through the block of polystyrene. (Your instructor may suggest an alternate way to stabilize the thermometer and test tube.) For a third trial, repeat steps 1–3, but this time, leave the thermometer in the chilled mixture while you pour ~5 mL (1 tsp) of chilled ice water (but without ice) into the test tube. Immediately place the chilled thermometer in the test tube, with the bulb totally submerged and held away from the sides and bottom of the test tube. Measure the temperature change for 20 min, using 30-s intervals.
More Things To Try Consider which conditions determine the rate of warming for chilled water. Predict what will happen when you change a particular variable, such as water quantity, the water surroundings (such as metal vs. glass containers), etc. Measure the warming of chilled water using the chosen condition. Did your results match your prediction?
Questions 1. Predict the appearance of a graph of temperature (y-axis) vs. time (x-axis) for the thermometer bulb in room temperature air (step 3). Where would the starting point (t = 0 s) and the final point be? What determines the final temperature? Would the line between the two points be straight or curved in some manner? 2. Graph the data from step 3, for the thermometer bulb in room temperature air. 3. How closely does the graph match your predictions from question 1? Speculate why there were differences. 4. Graph the data you collected in steps 4 and 5. Will all three graphs end at the same temperature? Why/why not? 5. Calculate and compare the slopes of the steepest portion of each graphed line. Suggest a reason for any differences. 6. Sketch what a warming curve would look like if ice were initially present in water. Explain the graph’s appearance.
Information from the World Wide Web (accessed Jan 2007) Who invented the thermometer? http://www.brannan.co.uk/thermometers/invention.html About temperature. http://eo.ucar.edu/skymath/tmp2.html This Classroom Activity may be reproduced for use in the subscriber’s classroom.
448B
Journal of Chemical Education • Vol. 84 No. 3 March 2007 •
www.JCE.DivCHED.org
photos by J. J. Jacobsen and R. J. Wildman
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