edited by: RON DELORENZO Middle Georgia College Cochran. Georgia 31014
Cinema, Flirts, Snakes, and Gases DAcio R. Hartwig and Romeu C. Rocha Filho Universidade Federal de SBo Carlos 13.560 SBo Carlos. SP Brazil The kinetic theory of gases simply states that gas molecules behave as infinitesimal points which move continually and randomly, suffering elastic collisions, the kinetic energy determined directly by the thermodynamic temperature. If the molecules are continually moving it is seen that the gas pressure is a consequence of their collisions with the walls of the container. g evert he less, the students immediately question why the pressure does not fluctuate since it is due to the individual impacts of different molecules. T o answer their questions in addition to explaining to the students that each gas molecule at 25'C and 1atm suffers around 1 X lo9 collisions per second, many with the wdl-an analogy with cinema can be introduced. In the cinema one has the sensation of "real" movement; actually, a series of still pictures is being nroiected on the screen. hut a t a rate (24 frames oer second) k h k h is greater than the human eye c& detect individually, which leads to the sensation of movement. Analogously, the gas pressure detected by a manometer does not fluctuate since the manometer, as haooens with the human eve in the case of cinema, is not suff&iently sensitive to respond to each of the many different impacts, hut only to their net result. Other student difficulties come up when the behavior of nonideal gases is analyzed. Why does the interaction between molecules become more significant as the temperature decreases? Why is the volume occupied by the molecules greater than their actual molecular volume? The first of these questions can he answered, considering our automohile-dependent societies, by the flirting motorist
analogy. A person who is driving a car along a street and flirting with pedestrians a t the same time, flirts (interacts) more efficiently at lower car speeds. At 50 miles per hour the flirtation. a t best. is verv tenuous: a t 5 miles oer hour the efficiency of the flirtation greatly increases. Going hack to the eas molecules. it is sufficient to recall that their kinetic enerw ys directly dependent on the thermodynamic temperature. Hence, the speed of the molecules decreases with a decrease in temperature and, analogous to the flirt, the interaction between the molecules becomes more significant. The second student question can he answered by recalling that molecules have a finite size. Because of this, the volume of a vessel containing a real gas is not only empty space, as happens for the ideal gasmodel. Consequently, a fraction of the volume of the vessel is not free space through which the molecules can move. This fraction is known as excluded volume,' since the empty space available to the molecules to travel in is not the total volume of the vessel hut a volume smaller by that fraction. This the students understand quite easily. However, they do not understand why this excluded volume is ereater than the actual molecular volume. This can he clarified through the iolluwing snnke analogy. If sudd~nlva venomous inukt. ar)l)ears it1 I he rniddlt, of a crowd, whatwill happen? ~mmediatelythe snake will have availahle an area ereater than its actual area. Whv? Because repulsive interacgons occur between the human beings and the snake. Analopouslv. .. . the same hauoens with nonideal pas rndecules. The repulsive interac~ionsoithe molecule^ xc&t fur the Fact that the occupied \.olume is lnrrrr than tht, i1ctt1:11 molecular volume. ~urthermore,the factthat the ratio hetween the excluded volume and the actual molecular volume varies for different gases can also be explained by this analogy, simply by varying the genus or the size of the snake.
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' When the van der Waals equat on is intrcduced, th s exc uded volume
mi$faamre presents a calleetion of applications and analogies which om readers have found to be usefulwhen peseming same of the difficuk a ~ e e p t frequently s encountered in chemisby. The blending of chemisby with Current applicationsand analogies places bath chemistry and student ima a familiar sening, stimulates nudent imerest,and produces an educated (versus trained) student. Contributions that will praduce a greater appreciation and knowledge of political, religious, economic, historical, and scientific aspects of life are encouraged.
is equal to rhe consranr b. n rhrs case the secono question above s
normal y answered rhrougha geomerrica mcdei tor spner cal rno ecuies which leads to an excluded volume b of four times the volume actually occupied by them. However, the comparison between volumes occupied by differentsubstances in the liquid andlor solid state@)with their b values leads to the conclusion that a "quantitative interpretation of the value of bas being four times the actual volume of the molecule is not justified [King. E. L., "Chemistry." Painter Hopkins Publishers, Sausalito, CA, 1979, p. 160.1. So, we think the above analogy to be of help then.
Volume 59
Number 4
April 1982
295
