In the Laboratory
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Thermal Expansion: Using Calculator-Based Laboratory Technology To Observe the Anomalous Behavior of Water Mario Branca* Dipartimento di Chimica, Via Vienna 2, 07100 Sassari, Italy; *
[email protected] Isabella Soletta Istituto di Istruzione Superiore “G. Manno”, via Carlo Alberto 92, 07041 Alghero (Sassari), Italy
According to Archimedes’ principle less dense layers of liquids rise to the surface while heavier ones sink to the bottom. Because liquids normally expand as the temperature rises, at deeper denser levels the temperature is usually lower. One important exception is water. In the interval between 0 ⬚C and 4 ⬚C water behaves in an anomalous way. Beginning at 0 ⬚C, the density of water increases as the temperature rises (Figure 1). At 4 ⬚C it reaches its maximum density. Above 4 ⬚C the density of water decreases as the temperature increases (1), as does that of all other liquids. Our experiment consists of following the changes in temperature at different depths in a precooled liquid while the liquid slowly warms up to the temperature of the surrounding environment. These measurements can be taken with bulb thermometers, but using Calculator-Based Laboratory (CBL) technology has obvious advantages. CBL technology is relatively inexpensive, easy to use, and easy to transport. By allowing the use of up to three sensors simultaneously, CBL enables real-time measurements to be made and the data are immediately displayed graphically to the students. Students can concentrate on analyzing the graph rather than constructing it and so are in a better position to connect what is happening physically with the results. In addition CBL measurements are taken at shorter intervals than manual measurements and there is a real synchronization of
the simultaneous temperature measurements taken at different depths. In this way the time lag between taking the measurements and interpreting the results is shorter. We have found that immediate use of results makes it easier for the students to understand and relate to the experiment. Didactic Relevance This experiment may be used in a course on temperature, on heat transmission, and in particular in the study of convection currents. The students must be familiar with Archimedes’ principle. All the measurements are easy to take and a laboratory setting is not necessary. The experiment may be carried out in a single two-hour period by groups of three or four students working in parallel on three different liquids. At the end of the lesson the students compare their results and come to conclusions on what they have observed through a group discussion guided by the teacher. Instruments and Materials Assuming that the class is divided into three groups one needs: • First group: water at a low temperature and crushed ice • Second group: 500 mL of cooled denatured alcohol (ethyl alcohol) • Third group: 500 mL of cooled cooking oil (sunflowerseed oil)
1000.02 1000.00
Each group needs:
Density / (kg/m3)
999.98
• A 35-cm tall, 500-mL cylinder
999.96
• An insulating cloth
999.94
• Two temperature probes
999.92
• A data acquisition system
999.90
The Texas Instruments data acquisition system consists of a CBL connected to a TI-92 computer graphic display.
999.88 999.86
The Experiment
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Temperature / °C Figure 1. Water density versus temperature.
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The two temperature probes are bound together with rubber bands so that the sensors that read the temperature are about 20-cm apart. The two probes are then inserted in the 35-cm tall cylinder taking care that the bottom probe is close to the bottom of the cylinder and that the probes do
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In the Laboratory
not move during measurements (Figure 2). The probes must not touch the bottom or walls of the cylinder. The data acquisition system is prepared and the time intervals and number of samples chosen. The precooled liquid is poured into the cylinder, which is wrapped in insulation to prevent the heat exchange with the environment being too rapid. The top of the cylinder is closed to minimize surface evaporation, and collection of data begins. In our experiment the measurements were taken for 45 minutes, with samples taken every 30 seconds, for a total of 90 readings.
Behavior of the Denatured Alcohol Denatured alcohol, 500 mL, was kept in a freezer overnight and then poured into the cylinder with the probes. While the system reached thermal equilibrium with the outside environment the temperature was taken at two different levels. The change in temperature during the 45 minutes of the experiment is shown in Figure 3. During the entire experiment the temperatures measured by the probes depended on their level. The highest temperatures were recorded by the top probe and the lowest by the bottom probe. The hypothesis that alcohol expands as the temperature rises and that the warmer layers rise to the surface was confirmed. Behavior of Cooking Oil Ordinary cooking oil, 500 mL, was cooled and the same experiment carried out. In this case it was not possible to begin with subzero temperatures as at these temperatures the oil became slushy. The results are shown in Figure 4. Once
again the temperature changes were regular and the temperatures recorded by the probe nearest the surface were greater than the bottom probe. Cooking oil behaves in a similar manner to alcohol.
Behavior of Water In the third experiment water at low temperature was obtained by mixing water with crushed ice. The behavior of the water was different from that of the other two liquids described above. The results show that at approximately 4 ⬚C the two temperature curves intersect (Figure 5). It can be seen that between 0 ⬚C and 4 ⬚C water behaves differently from the other two liquids. The bottom probe consistently registered higher temperatures than the top probe. The lower, denser strata rather than being colder, as was the case in other
Figure 3. Temperature changes over time in denatured alcohol in a cylinder, recorded by probes at two different depths.
Figure 4. Temperature changes over time in cooking oil in a cylinder, recorded by probes at two different depths.
Figure 5. Temperature changes over time in a cylinder filled with water, recorded by two probes at different depths. The broken line is the lower probe and the solid line is the upper probe.
Figure 2. Probes and cylinder.
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liquids, was warmer (Figure 6). Once the temperature rose above 4 ⬚C, where the curves intersect in Figure 5, the water behaved in the same way as the other liquids and the upper layers were warmer and less dense.
Tt Tb
Conclusions At the end of the experiment there should be a discussion period where the students describe their results to the rest of the class. What the students should notice is that when the oil and alcohol became warmer they expanded and the warmer layers moved to the surface as would be expected from Archimedes principle. By contrast water behaves differently, as can be seen from the fact that the curves cross (Figure 5). This anomaly is due to the fact that water becomes denser between 0 and 4 ⬚C and thus in this temperature range the colder layers are less dense and the higher temperatures are found at the bottom. Above 4 ⬚C water behaves in the same way as the other liquids, as can be seen from the graph. The instructor may like to point out how this anomalous behavior is of vital importance for the existence of life on earth. In addition, presenting the data from the three experiments on one figure (Figure 7) can be used to emphasize the following:
Figure 6. Temperature changes in water: above 4.0 °C Tb < Tt, between 0 °C and 4 °C, Tb > Tt. (Tt is the temperature of the top probe, Tb is the temperature of the bottom probe.) A
B
• There are always temperature gradients in a liquid as it heats or cools. The liquid has the same temperature throughout only if it is stirred or after thermal equilibrium has been reached. If the liquid is not in thermal equilibrium and is heating or cooling there will be zones inside it where the temperature is different. In water between 0 ⬚C and 4 ⬚C the temperature decreases from bottom to top while above that temperature the opposite is true, as is the case for other liquids. • Water is not a good thermometric liquid. The behavior of water is anomalous between 0 ⬚C and 4 ⬚C. Oil and alcohol are better thermometric liquids. In addition alcohol does not change state even at low temperatures and is therefore the most suitable of the three for use as a thermometric liquid. Furthermore water is not very sensitive to temperature changes, is very thermically inert, and needs more time to reach environmental thermal equilibrium. • Water has high specific heat. The temperature varies more slowly with time than for the other two liquids.
Thus this laboratory experiment helps the students to increase their knowledge of the concept of specific heat, the mechanisms of convective currents, and Archimedes’ principle. Possible Hazards Denatured alcohol is poisonous and extremely flammable. Adequate ventilation must be used.
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Figure 7. The graphs for cooking oil (A), alcohol (B), and water (C). The temperature scales used and the time scales are identical.
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Supplemental Material
Detailed instructions to setup and run the CBL and calculator are available in this issue of JCE Online. Literature Cited 1. Stott, V.; Bigg, P. H. In International Critical Tables of Numerical Data, Physics, Chemistry and Technology; Washburn, E. W., Ed.; McGraww-Hill Book Company: New York, 1928; Vol. III, p 25.
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