the comnuter bulletin board ming. They also "discover" some new ideas, including the computer as a powerful tool.
Stoppmgour "experiment" for a moment, we discuss thc Einstein and Debve models for the heat cwacltv of solids. Einstein treats tLe atomic vibrations in asolid using the simplifying approximation that assumes that each atom vibrates independently of the others with a common angular frequency w (7). Afterwards students compare their data with the prediction of this model by just writing the expression in MathCad.
where OE (Einstein's temperature) is left as a parameter of the solid. At first sight the students would say that the model correctly fits the data (this can be done with OE= 140 K) predicting the zero value of C,, but we ask them to change the temperature scale to a value lower than 100 K, obtaining a plot similar to Figure 2. Obviously, the model does not predict the p law for any value of OE. For Debye's model we take the freouencies of each oscillator w; to range ~ontinuouslyover the valueawo > &; > 0, and we get the following expression for C, (8).
Computer-Interfaced Apparatus to Study Osmosis and Diffusion John N. Fox, Kenneth Hershrnan, and Terry Peard
College of Natural Sciences and Mathematics Indiana University of Pennsylvania Indiana, PA 15705
Project EXCELS (Expanding Computer Education in Learning the Sciences) has been supported for a number of years by the National Science Foundation. The Proiect works c~ntinuouslyto develop experiments that can be carried out by - hiah - school students using- com~uterinterfacing (9). There are certain studies that lend themselves to computer interfacing, and the maximum benefit is derived using computer interfacing. The computer is used as a laboratory tool that either captures what cannot be seen or replaces the tedious task of data collection. Computer in(Continued on page A2601
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where OD is the Debye temperature (215 Kfor Ag). Figure 2 shows an excellent fit. Even aRer changing the scale there is no problem; the data remains fitted. Cv 1 At last we ask our students to compare the A parameter of their cubic fit with that obtained from the Debye ( cO1/molK) model when T goes to zero for their 'lO law with that obtained approximating the i n t e ~ ~when a l T approaches zero.
As we would expect, the quantummechanical models differ from the classical result only at low temperatures. Both the Einstein and Debye models predict that the heat capacity of a solid should go to zero as T goes to zero. However, the Einstein model predicts much lower values of C, than does the more realistic Debye model, which also predicts t h e so-called Debye's 'lO law. Conclusion
n "
0
b
----
-
EXPERIMENTAL DATA T~LAW EINSTEIN MODEL
DEBYE MODEL With the aid of MathCad our stuand carry Out dents can plot, Figure 2. Einstein and Debye models forthe heat capacity and experimental data of solid Ag. merical integration without programA258
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the comnuter bulletin board
TIME
Figure 1. The pressure sensor and its amplifier. The output from the amplifier goes to the advanced interface board (AIB).The AD524 is an instrumentation amplifier.As pictured, the gain of the amplifier is set for 1000. However, this amplifier can be used as either a singleended or differential amplifier (as pictured) with a gain of 1, 10, 100, or 1000.
(SEC.)
Figure 3. Aplot of the pressure increase (proportionalto the amplified output voltage from the pressure sensor) as a functionof time due to the passage of water into the water and molasses solution.
MoIasse* and W a t e r Solution *If Membrane
Olrtllled Water
Figure 2. Apparatus for measuring the rate of diffusion of water across a dialysis membrane into a water and molasses solution.
terfacing gives students the time to study variations of an experiment. We believe that computer interfacing offers the student the best opportunity available a t the high school level to learn hands-on science and to experience the scientific environment. Two particularly interesting experiments are described below. l h r firsr deals with osmosis and the second with gas diffusion. Both exoeriments use the MultiPumose Laborstory Interface from Vernier Software.' However, any one of a number of interface units could be used including that from PASCO scientific2 or the Universal Laboratory Inter'Vernier Software, 2920 S.W. 89th Street, Portland. OR 97225. 2PASC0 Scientific, P.O. Box 619011. 10101 Foothills Blvd, Roseviile, CA 95661-9011. 3MPX100A~available from Newark Electronics, 9800 McKnight Road, Pittsburgh, PA 15237-6091.
Figure 4. The rate of osmosis is proportional to the best straight-line fit of the data in Figure 3. The rate of osmosis is plotted for three differentconcentrations of water and molasses solution. The rate of osmosis increases linearly with the concentration of molasses in the solution. face' for the Macintosh. I n the experiments described below, data is accumulated over a brief time so that several studies can be done by the high school student in the usual 40-min laboratory period. Both experiments make use of a pressure ~ e n s o rThe .~ sensor and its amplifier, an AD524 instrumentation amplifier,' are illustrated in Figure 1. A similar packaged pressure unit is available from Vernier Software.
Studying the Rate of Osmosis with Molasses
To study the rate of osmosis, one end of a plastic or glass cylinder is closed off by attaching a piece of dialysis membrane to the end with silicone sealant. A rubber stopper containing a narrow glass tube is fitted to the opposite end of the cylinder. Before inserting the stopper, the cylinder is filled with a molasses solution, making certain that the (Continued on page.4262)
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the computer bulletin board level of the molasses always rises to the same starting point on the narrow glass tube. The pressure sensor is attached to the glass tube. Then the end of the cylinder with the attached dialysis membrane is placed just below the surface of a container of distilled water, as shown in Figure 2. The data in Figure 3 illustrates the pressure change (proportional to the output voltage from the AD524) in the air space above the molasses versus time as water diffuses across the membrane into the water and molasses solution. Figure 4 displays the rate of pressure change, obtained using the best-fit straight line to the pressure versus time eraoh. Dlotted acainst the various concentrations of the morasses'and wat& solution. Clearly, the rate of diffusion of the water across the membrane is a linear function of the concentration of molasses and water solution. Studying Gas Diffusion with a Flower Pot
Another study done using the pressure sensor concerns gai d i f f u ~ i o n tthrough l~~ a-poro& material. The open end ofan unglazed clay flower pot is attached to a sheet of plastic or other material usingdiwne sealant. A pressuresensor is attached to the inner region of the pot through the pot's drain hole using a rubber stopper. A large inverted container is flooded with helium gas and placed over the flower pot.
TIME (SEC.)
F gbre 5. Press~remange nsoe the f ower pot wnen me ne Idm gas ddlJSeS nto tne pot an0 alr o limes OJI of tne pot
Figure 5 illustrates the data collected over several minutes. The pressure inside the pot rises rapidly as the helium diffuses into the pot, but eventually the slower-diffusing air inside the pot escapes and the pressure falls. Later the pressure falls below its starting point because some of the helium in the glass beaker surrounding the pot escapes. This allows the helium inside the clay pot to diffise outward, causing a partial vacuum. Conclusion Both of these experiments are easy to carry out and have a good deal of latitude for further studies. For example, if the clay pot is heated, does the peak in the diffision curve chance Dosition and whv? How will the rate of osmosis vary with the temperature of the system? Computer interfacing experiments such as these turn a high school laboratory into a research laboratory for students, affording them the same excitement of diswverv that research scientists find every day in laboratories thioughout the world.
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Acknowledgment This work is su~oortedthrough a a a n t from the National Science ~oin'dation ~ o . ' ~ 1 ~ ~ - 9 0 5 3and 764, Ind~anaUnivcrs~tyof Pennsylvania. Literature Cited 1. Streitwiener. A. Molecular O r b ~ h Th-3 l 2. 3. 4. 5. 6. 7. 8.
/or Organic Chemcst-; W~ley:New Yorh. 1961. Farrel, J. J.: Haddon, H.H. J. Chem. Edur 1989.66.839. Wismer,A. l%trahdmnComp. Mefh. 1980.3,63. Heilbmnner,E.; Boek, E. ThaHMOModeiandit-Applicoiion; Wile?: New Yark, 1976. Van-Catledge. F A . J Org. Chem 1980.45, 4M1. G a z i e ~A. , R. ZBosic-lnteractiueBAS1C Compiler; Zedcor, Inc;k s a n , A Z . Barmw G. M. Phyatal Chem&Lv.3rd d.: New York,Mffiraw-Hill. 1973. Jackson,A. E. Equil1b"um SLot&lieolMpehonics: Pmntiee-Hall: Englewood Cliffs.
fromvernier SoRware in 1998. 10. Key,R.: DePaola, B. D. "ASimple ApparatusforDemonshationofGaseous Diffusion' Phys. Roch 1631,29,52%523. A262
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