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GEORGE L. GILBERT DeniSm University Granville. Ohio 43023
A Simple Device to Demonstrate the Thermal Conductivity of Gases S U S M ~BYE O E. Koubek U. 5. Naval Academy Annapolls. M D 21402
C. L. Braun Dartmouth College Hanover, NH 03755 CHECKED SY
Fred Juergens University 01 WISCOMIII Madlson. WI 53708
Demonstrating the differences in the thermal conductivity of gases is certainly not a new idea. In fact, the idea appears to have originated as early as 1808 when Dalton measured the time reauired for a heated thermometer to cool the same number bf degrees in different gases. During the years that followed many investigators carefully studied the thermal properties of gases, some using equipment similar to the device we intend to discuss here.' Today most physical chemistry texts, and even a few freshman texts, discuss the thermal conductivity of gases. In these discussions the coefficient of thermal conductivity, K , is usually shown to be equal to ncCvX/3where n is the gas
number density, E the mean speed, C, the constant volume heat capacity (per molecule), and X the mean free path. We have found that it is possible to demonstrate the contribution made by each term in this expression by using the simple apparatus shown in Figure 1.This apparatus we feel renresents an im~rovementof a similar device revorted earlier by J. W. ~ a r i e r . ~ First we fill the glass tube surrounding the nichrome wire with argon and tuin up the Variac untg the wire begins to glow. (Caution: The outside of glass tube can become quite warm. Also, the metal parts are electrically "alive.") Then we flush out the argon with helium and watch the glow disappear. Most students will quickly realize that the result occurs because helium atoms, being lighter than argon atoms. travel faster and the ereater e. the ereater K. It then follows that the greater the r i t e of en& tFansfer, the cooler the wire. However. some of the studentsmav also realize that the same simple kinetic theory thatleads to^ = ncCJ/3 also For a brief historv and an indeoth treatment of this tooic see:
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P~ltinot0t7 .I . R "An ..Advanced ~reaiise ~hemisth." -. .. - ~ -~on Phvsical , . Vol. 1,2nd ed., Longmans, London, 1962; p 888. Barker. J. W., "Tested Demonstrations in Chemisby," 6th ed., Division of Chemical Education, Easton, PA. 1969; p 142. ~~
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vacuum Gauge
Joint Wllh
Brasas
Rubber
0-Ring
20 Gauge Nlchrome Wire
2.8170cm
Glass Tub.
Weighled Brass Sleeve
Figure 1. Thermal conductivity apparatus.
Figure 2. The weighted "sleeve" electrical connection.
Volume 63
Number 3
March 1986
267
yields A = l/(sp2n), where p is the molecular diameter, and therefore one may also write K = EC,/(3rp2). Expressing K in this form makes it evident that the greater speed of He is not the only factor leading to an increase in thermal conductivity. Clearly one must also consider the fact that He has a smaller molecular diameter than AI.~ Next we replace the He with CO?. Now, even though the molecular weight and molecular diameter of CO, are greater than those fo; Ar, and thus COz should travelslower and have a shorter mean free path, the wire will refuse to glow as brightly as before.4 This usually surprises students and encourages a discussion of C, for COr versus Cvfor Ar.5Finally we remove the CO? from the tube hv connecting the svstem to a water aspirator. However, before actually turning on the water aspirator, the students are asked to predict the effect of decreasing n, the number of molecules per unit volume. Most predict that the wire will glow still brighter because many have learned that a vacuum is a good in&lator. When the water is turned on and they see the gauge recording a vacuum, they are again surprised by the result when they see to the wire. I t may again he necessary that nothing. happens .. topomt out that the mean free path is inversely proportional to n and that unless one pumps out "nll" 01 the molrrules of CO2 not much is to he e ~ p e c t e dThis . ~ can lead to a discussion of the descriptive chemistry of "getters" and their use in large vacuum flasks. Although the apparatus shown in Figure 1was fabricated in a machine shop, a similar device could undoubtedly be constructed from plain glass tubing and rubber stoppers. The reason for the weighted "sleeve" electrical connection (see Fig. 2) is to keep the rather heavy. gauge - - nichrome wire taut a s it is heated 20 prevent it from sagging and making
268
Journal of Chemical Education
contact with the sides of the glass tube. The inside of this sleeve is slightly larger than the outside diameter of the guide tube but by tilting the entire apparatus slightly, continuous electrical contact is maintained as the sleeve moves up or down. The inner 24/40 joints are machined brass and are grooved to accommodate two rubber O-rings. These provide a good vacuum seal without grease. = A l t h w the 6 difference is the dominant effect, (4014)'12 = 3.1, the size difference between the atoms contributes = 1.7,to the overall effect xMlna, significantly,p:,lpk = (3.4)2/(2.6)2 u -. 6 -
The effectis not as dramatic as when He was substituted for Ar but may definitelybe seen, especially in a partially darkened room. Actually, in spite of the previously mentioned fact that c4, > eq and pco, > p*, the values of x for Ar and Copat 0°C are almost the same. The respective values are 38.8 X and 34.3 X 10-6 callscm°C (Moore. W. J.. "Physical Chemistry," 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, 1962: p 225). The larger value of C, for GO2. 6.73 calIm~l-~C, compared to 2.98 callm~l-~C for Ar almost compensates for the mean speed and diameter difference. However, at the temperature of the hot wire. C, for GO2 increases substantially due to an increased contribution from vibrational modes. This of course is not possible for the monoatomic Ar: its value remains constant over the temoerature ranae of interest in this demonstration. .~ Tnus, tnis demonstrat8on shows not only lhe conlrioLlion maoe by hear capacilies to thermal conductwities out also lhe effecttemperature may have upon the relative value of K for po yalom c as compared to monoatomic gases. Wore correctly one needs to produce a vacuum in which A is comparable tow largw than the distance between the wire and the glass wall before a substantial decrease in thermal conductivity may be expected. In our case this distance is about 12 mm so a pressure of at least torr must be attained.
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