edlted by GEORGE L. GILBERT Denison University Granville, Ohio 43023
Balloon Balance Thermometer A Lecture emo on strati on of Charles's Law
Balance Readings versus Bath Temperature Balance reading
Water bath temperature
-Submitted by:
and C. W. ~ e & T h e Ohio S t a t e Universitv Columbus, OH 43210 Richard F. Jones Sinelair Community College Dayton, OH
Checked by:
A simple but dynamic illustration of Charles' law with a balloon-balance thermometer allows a speedy determination of the absolute minimum temperature to within an accuracy of 10%of the exact value -273.15'C. In addition to the kinetic theory of gases, theories for liquids and for rubber solids may be utilized in discussing the results of the experiment. Concept The balloon-balance thermometer makes use of air as a thermometric fluid, a water bath as the thermometric vessel, and the readings of a triple beam balance as a thermometer scale. According to Charles' law, the volume of a balloon increases linearlv with water bath temperature of the gas in the balloon 3$10n;a~thrgils pressurean.d thc elastivit~bfthe l~illloonarc cmstnnt. IJnder thvse condit~tms,the huiwant force acting on the balloon, and hence the balance reading S, should also change linearly with bath temperature T. Variations in buoyant forces arising from the dependence of liquid density upon temperature are neglected. The ohvsical significance of the constant B is c o m ~ l e xbecause there are several volume restoration forces, namely, rubber elasticitv. surface elasticitv of the liauid surroundine the balloon, a n d the water head: ~ c c o r d i n gto the kinetic theories for rubber solids and for liauids. . . restoration forces in the rubber wall of the balloon increase with increasing temperature24 whereas restoration forces in the water-balloon intrriwc decrenst. aith inmming temperarurr.'A hydrwtatic aatcr hexi of O.UO': atln act-: as ;I negligible restor;ltion force
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Bollaon B o l o n c a
of
Thermometer Demondralion Charle's Lou
upon the walls of the balloon when immersion depths of approximately 8 cm to balloon center are used. In the simplest approximation, one might expect that where A is the balance reading a t zero temperature on the Celsius scale. Equipment The necessary equipment consists of the following: (1) an air-inflated balloon; (2) a set of weights or anchors which are sufficient to submerge the balloon in a water bath; (3) a laboratorv* t r .i ~ l ebeam balance to record the combined weight of the submerged balloon and anchors for several different bath temneratures: (4) several refilled beakers containing the same amount ofwater but each at a different temperature. (The quantity of water should be sufficient to completely submerge the balloon and its anchor.); (5) string to support the balloon and anchor from beneath the pan side of the triple beam balance; (6) a Celsius thermometer operating in the range O°C to 100°C for determining the bath temperatures just prior to submersion of the balloon and anchor. Results Typical balance readings, S (grams), versus water bath temperature T ("C)are presented in the figure for three different balloon-anchor svstems. Above room temperature, there appears to be significant curvature in the Sbersus T plots. but in the region from ice bath temperature to room temperature, S appears to be a linear function of temperature. Results for Balloons #1 and # 2 were obtained prior to the classroom demonstration in order to define suitable calibration temperatures for the balloon-balance thermometer. In these preliminary experiments as many as seven data points for each balloon were obtained. Balloon # 3 was used in the classroom demonstration, and the resultant data are aiven in the tahle. If an extension to lower teml~crart~rrs i ? dcsired, it is rmwnienr to us(: an antifree~elwnterbath liquid instead of water. 'l'he preliminary experiments showed that suitable accuracy was obtainable without a sub-zero measurement, so only two temperatures, namely 6.6 and 22.5 OC were used for the classroom demonstration. As an alternative to graphical analysis the two data points were used to calculate A and Bdirectly. Evaluation of A and B requires the solution of two linear Paper submitted August 16,1978.
' Present address: Department of Chemistry, Virginia Polytechnic
Institute and State University, Blacksburg, VA 24061. Stein, R. S., J. CHEM. EDUC., 35,203 (1958). "reoar. L. R. G.. "The Phvsics of Rubber Elasticitv." Oxford New York. 1949. ~niversitv~ress. ' ~ , , r , d kF. ~ n Fryd. d .\I,. I ('HEhl. EDtl('., 35, Slh,lYSol. " .\lurrimrr.C'. F . " ( ' h ~ m i ~ l r.Ay C ~ m w p t i m n,\ppnmch", l :lrd ed., I). \'an Nostrand ('mnl,;~n.s,Ntu, York, 1975, p I'M.
e..
Typical data for three anchoring systems
Volume 56, Number 12, December 1979 / 823
A value of T,:, = -272.2"C is obtained using the data in the table. This result is fortuitously close to the accepted value of -273.15'C. Corresponding values of T,;, obtained with balloons # 1 and # 2 are in error by about lO%,which is considered satisfactory within the limitations of the model.
equations. The obtained A and B values are A = 248.3 g
and H = 1.044 g/OC
The maximum balloon-balance thermometer reading, S,, corresponds to zero buoyant forces acting on the balloon (zero balloon volume) and is simply the balance reading when the the liquid bath but with the anchor balloon issupported remainingsubmerged,~h~ value, s,, = 532.5 g, was obtained fur the balloon-anchor system used in the classroom demonto zero-halloon vol. stration. since this reading rime, the resultant bath temperature calculated using eqn. (1) using a gas defines the lowest temperature, T,:,, thermumeter.
T,,.
= ( A - Smax)IB
824 / Journal of ChemicalEducation
(2)
~i~~~~~~~~
Several authors'.4 have discussed the inflation of toy balloons a t constant temperature, but neither the relevance to Charles' law was noted, nor was the importance of the rubber-liquid interface elasticity. Stein' suggests that the volume ofthe balloon should be independent of temperature since gas pressure and balloon elasticity are each proportional, but in inverse ways, to the absolute temperature. The present data does not support Stein's suggestion. Instead it demonstrates the imnortance of elasticitv in the rubber-liuuid interface, and particularly its temperature dependence.'
