LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Demonstrating the Temperature Dependence of Density via Construction of a Galilean Thermometer Marie A. Priest, Lea W. Padgett, and Clifford W. Padgett* Department of Chemistry and Physics, Armstrong Atlantic State University, Savannah, Georgia 31419, United States
bS Supporting Information ABSTRACT: A method for the construction of a Galilean thermometer out of common chemistry glassware is described. Students in a first-semester physical chemistry (thermodynamics) class can construct the Galilean thermometer as an investigation of the thermal expansivity of liquids and the temperature dependence of density. This is an excellent first laboratory for physical chemistry as it generates student interest; plus, it is a green experiment only using water, food coloring, and glassware that can be recycled from year to year. The thermometer can also be constructed without a detailed discussion of the mathematics behind it, making it accessible to general chemistry students. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Applications of Chemistry, Physical Properties, Thermodynamics
Galilean thermometer,1 whose invention is credited to Galileo Galilei, is a thermometer made of a sealed glass cylinder containing a clear suspension liquid with a number of floaters suspended in it. Commonly, those floaters are themselves sealed glass containers filled with colored liquid for an esthetically pleasing effect, but in principle can be anything with an appropriate density. This thermometer is based on the principle that density changes with repect to temperature, allowing the floaters to be built with a fixed density (that is relatively constant due to the small thermal expansivity of borosilicate glass). As the temperature of the suspension liquid changes, its density changes, and the suspended floaters rise and fall depending on their density. If the suspension liquid chosen has a known density as a function of temperature, the floaters can be designed to float at a set temperature. For example, if water is chosen for the suspension liquid, one can use the following density equation of state,2
A
Fwater ¼ a1 þ a2 C þ a3 C2 þ a4 C3
in a thermodynamics-based physical chemistry class that normally starts with thermometry as an historical lead-in to the laws of thermodynamics. The construction of the Galilean thermometer is a flashy experiment (Figure 2) that gets the attention of the students and is a green experiment requiring only water and grocery store food coloring as chemical reagents. All of the glassware can be reused from semester to semester. The experiment also stresses the importance of accuracy in the lab setting to achieve the desired results.
’ EXPERIMENT A dry, 13 mL glass centrifuge tube with ground-glass stopper was weighed. A very small quantity of silicone grease was applied to the glass stopper (to ensure a water-tight seal), the excess grease was wiped off, and the stopper securely inserted in the tube. The tube and stopper were reweighed. The centrifuge tube with groundglass stopper was completely filled with water of known temperature and weighed. The mass of the water and the density of water at the known temperature (calculated from eq 1) were used to calculate the internal volume of the centrifuge tube; the density of Pyrex glass (2.23 g/mL)3,4 was used along with the mass of the tube to determine the volume of the glass. A piece of 24-gauge wire approximately 10 cm in length was accurately measured to determine its mass and length, then wrapped around the neck of the glass stopper to use for fine calibration. The wire was assumed to have a density of 8.0 g/mL and its volume was calculated. These three volumes give the total volume of the floater. Students were given a target temperature for their floater; using the density of water at the target temperature (obtained from eq 1), the student
ð1Þ
where the C is the temperature in degrees Celsius and the ai’s are constants used to fit the equation to experimental data with the following values: a1 = 0.99989; a2 = 5.3322 105; a3 = 7.5899 106; a4 = 3.6719 108. The ai values have units that provide density in grams per cubic centimeter (g/cm3). This equation is accurate to five decimal places over the range from ∼10 to 40 °C and to three decimal places over the entire liquid range (0100 °C). A plot of this equation over the liquid range of water is shown in Figure 1. Whereas the density of water varies very slightly with pressure, this equation is fit to experimental data at 1 bar and should be sufficiently accurate at pressure near 1 bar. In this experiment, students learn about the effect of temperature on physical properties, which is the foundation of the field of thermometry. The experiment is an ideal first exercise for students Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
Published: May 05, 2011 983
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thus possible to overshoot the mark, especially if the water bath is not adequately stirred to reach thermal equilibrium after adding cold water or ice. Gently nudging the floater can address this problem. Also, the surface tension of the water bath can lead the students to believe that their floater is floating in the hot water even when the density is such that it should sink. Simply pressing the flask below the surface of the water will eliminate this source of confusion. If the neutral buoyancy temperature was different from the target temperature, the change in mass needed to correct the density of the floater was determined, and a length of wire with the correct mass was removed (or added). The neutral buoyancy temperature was rechecked after the modification of the calibration wire.5 The floaters produced by the class were assembled in a 2 L mixing cylinder filled with degassed room temperature water. Each floater was labeled with permanent marker as to the temperature it was designed to indicate. The cylinder was topped off with water and fitted with a glass stopper (Figure 1).
Figure 1. Plot of the density of water as a function of temperature, at 1 bar; points are values from CRC Handbook;2 the solid line is eq 1 fit to those experimental data.
’ HAZARDS There are no hazards associated with this experiment.
Figure 2. A Galilean thermometer constructed from centrifuge tubes.
calculated how much the floater must weigh to have the density of water at their target temperature. The total mass needed to obtain that density was determined given the floater volume calculated above. The students added a sufficient volume of colored water to obtain the correct total mass, iteratively weighing and adjusting the water level until the desired value was reached (students could easily get within 3 mg, and most could get within 0.5 mg). At this point, the floater was roughly calibrated and ready to be tested. A large beaker was filled with enough hot (3540 °C) tap water to fully submerge the floater (a small amount of the wetting agent 2-methyl-2-propanol can be added to the hot water to reduce the ability of air bubbles to stick to the floater). When the floater is inserted into the hot water, it should sink; if not, the previous step must be checked. A small quantity of ice or cold water was slowly stirred into the hot water, and the temperature was measured with a mercury thermometer with a precision of 0.01 °C held in the water with a buret clamp on a ring-stand. Once the currents in the water had stopped, the buoyancy of the floater was observed, and the temperature at which the floater started leaving the bottom of the beaker spontaneously was recorded. Attention should be paid to the fact that if the floater is on the bottom of the beaker it may not spontaneously rise when it becomes neutrally buoyant, but will rather experience no net force up or down. It is
’ RESULTS AND DISCUSSION Because this is a density exercise, mass and volume must be controlled for the floaters. Several different combinations of glassware were tested with varying results, as discussed in the Supporting Information. Centrifuge tubes with glass stoppers were determined to eliminate most sources of error associated with the equipment. The stopper returns to the correct position when replaced and does not trap air bubbles in the seal. In addition, the volume can be accurately calculated because the densities of all the components are known. The drawback to the centrifuge tubes is that grease must be used to create a water-tight seal after completing the calibration. This exercise can be used to demonstrate how changes in temperatures affect density. Physical chemistry students were also asked to calculate the coefficient of thermal expansion for water by taking the first derivative (see data in the Supporting Information) of the empirical equation (eq 1), and comparing this to literature values (and values they measure in a separate experiment). Students were also asked to determine if water has the same density at more than one temperature and how this will affect the ability of a Galilean thermometer to tell the correct temperature. Calculations were performed to find the temperature at which water is most dense, and students had to rationalize what is causing this behavior. Finally, students were asked to comment on ways to improve the accuracy of the thermometer; for example, which liquid, water or ethanol, would make a better thermometer and why. Physical chemistry students were given density data from the CRC Handbook2 and used that data to determine the parameters in eq 1 by fitting eq 1 to experimental data. For general chemistry, students could be given a table for the density of water as a function of temperature (see the Supporting Information). A simplified version of this experiment could be done without the use of the calibration wire if there is no desire to build a Galilean thermometer. Students using this method should be able to build a floater with an error of (6 °C without using a calibration wire or (0.2 °C using one. Further analysis of the errors involved is in the Supporting Information. When errors in the floaters are 984
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small, a thermometer built from them has a slow response time (two or more liters of water is slow to reach thermal equilibrium with its surroundings) but is still an attractive working thermometer. Five laboratory sections of physical chemistry students have used the procedure described above. Students in groups of two are easily able to make a floater in a 4 h lab period (most could do it in less than 3 h). Students thought it was “cool” to build something they had all seen in the store; many of them were surprised to learn how it worked, most assumed that each floater had a different liquid inside it. After doing the lab, two students decided to make their own Galilean thermometer from materials purchased online. Students did complain about the tediousness of measuring the neutral buoyancy temperature of their floaters. Overall, physical chemistry student reactions to the lab were positive.
(5) The calibration wire can be omitted and the student can see how close they can get to the target temperature, if there is no plan to construct a working Galilean thermometer.
’ CONCLUSION We present an attractive exercise that was designed to be a fun demonstration of the temperature effects on density and was implemented in the first semester of physical chemistry (thermodynamics). Emphasis was also placed on attention to detail in labwork and the determination of realistic sources of error. To date, five physical chemistry lab classes have used this experiment and each lab built a working Galilean thermometer (each ranging from 20 to 26 °C in 1 °C increments) as determined by comparison to a standard laboratory mercury thermometer. Students typically can calibrate the thermometer to within (0.2 °C. Although it has not been tested in a general chemistry laboratory setting, the authors believe that this exercise could also be easily adapted as a general chemistry laboratory exercise by excluding some or all of the mathematical analysis (see Supporting Information). ’ ASSOCIATED CONTENT
bS
Supporting Information Physical chemistry student handout (two versions); general chemistry student handout; notes for the instructor. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: cliff
[email protected].
’ ACKNOWLEDGMENT The authors would like to thank Todd Hizer, Suzanne Carpenter, Catherine MacGowan, and Delana Nivens. Funding for this work was provided by Armstrong Atlantic State University. ’ REFERENCES (1) Galileo thermometer. Wikipedia: The Free Encyclopedia. http:// en.wikipedia.org/wiki/Galileo_thermometer (accessed Apr 2011). (2) Equation fit to experimental data obtained from the CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.;CRC Press: Boca Raton, FL, 1991; pp 68. See Supporting Information for fitting procedure. (3) National Institute of Standards and Technology Website. http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=169 (accessed Apr 2011). (4) Instructor also measured the density of the specific glassware used to improve the accuracy of the experiment, see Supporting Information. 985
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