LETTERS A Call for Slmpllficallon
To the Editor:
To the Editor: In response to the article "An Instructive Gibbs-Function Problem" by V. Schomaker and J. Waser 11988, 65, 9681, I agree with the authors that the prohlem discussed is a challenging one (possibly even for the most capable students). I do nor believe. thotleh. that it is oarticularl\f instructive for most students', many bf whom dill not grasp the essential point of the problem even after studying tho authors' painstakingly detailed explanations. While I take exception to some of the authors'assertions. I have to conclude that their arguments are essentially sound. However, the complexity of the explanations I believe unduly obfuscates the matter, and this realization naturally ohligated me to attempt my own "enlightening" account. The problem in question was stated by Schomaker and Waser as follows: A liquid sample of, say, ether iscantained,withsome of its vapor, in
a thin-walled rigid bulb that is placed in a larger evacuated rigid elass vessel immersed ins thermostat bath held at tern~eratureT-. The largr wssel is *haken to l m a k the bulb, and some but nor dl of the liquid evnporatrs. With TI= T = 7',, and PI = I ' = P.,, one readily sees that A t i , , s , is ZWU. BUIthe process is clearly irrcverr. ihle. Why is AG,,h,, not less than zero? ~~~
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At first. I tboueht I'd come UD with a brief. incisive account based on aproof of falsity of some underlying assumption or the like. The best I have to offer after the expenditure of a reasonable amount of time is contained in the following two observations. The first is more concise, hut less convincing: the relation AG = 0 contains, in the limit, AG < 0; that is, AG = 0 is a sufficient condition for somethine - to haopen . spontaneously, albeit, under practical conditions, infinitely slowly. Second, since "AGether" = 0, yet a spontaneous process occurs, we must conclude that the "ether" by itself does not comprise the whole system. The authors also pursue this notion Gut in the process invoke, among other rhinyy, the properties of the container, whichclearly haw nothing todo with the oroblem.,neelieihle as their effect mirht be. According to t h k latter approach, the change in G f i r the system is the zero change for the ether plus that for the reservoir supplying heat for the vaporization. Since the heat supplied is (formally) a t constant volume rather than at constant = pressure as required for G to be constant, AG,.,,i, -PAV, and therefore AG,,, < 0. But to the "essential point", which is that G is defined so as to include "PdV" work. So, if we carry out a change in which we deliberately preclude this work, even though it be at constant pressure and temperature, obviously the driving force will exceed that accompanying a reversible change between the same limits. This is what necessitates the inclusion of the reservoir as discussed above. Finally, I also feel obliged to object to the authors' use of the terms "monobarostatic", "monothermostatic", "isobarostatic", and "isothermostatic". While I admit the terms "isobaric" and "isothermal" are ambiguous in the sense identified, I am unwilling to admit that the problem is ameliorated bv the introduction of vet ootentiallv more ambieuous terms t i a t also conflict withihekxisting ones.
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California
Donald Peterson State UniversiV. Hayward Hayward. CA 84542
In order to annlv .. - the Gibbs-function criterion. we must regard the system as comprising container and contents and also consider the orooerties of the container. (The analvsis would be different if the container were appreciably flexible or if i t included a turbine and dynamo, as mentioned below.) Moreover, the condition specified is that the reservoir fluid exert a constant pressure. I t is only our assumption of container rigidity that renders the system a c o n k t - v o l u m e system. Contrary to Peterson's assertion, the change in G of the reservoir is zero, with no change in P V and exactly counterbalancing changes in Uand TS. "G is defined so as to include ' P d V work" needs to be restated as "AG includes workPAVdone on the surroundings", but that doesnot help us to understand Peterson's nenultimate o .a r a-m a.~ h . With respect to AGCont.i,., (AG,la,, in our article), it might have helped had we discussed a related simple problem: an evacuated cylinder fitted with a sticky plunger. When the piston irreversihlv moves inward throueh volume V, work PV is done on the-system and energy PV-is lost thermally to the surroundings. The net effect is that Uis unchanged, as is S; AG is simply -PVby the definition of G and is negative in agreement with the irreversibility and the isothermostatic and isobarostatic conditions. (These are the general conditions for "AG < 0", in contrast to the overly restrictive, commonlv stiodated conditions-that the orocess should be isotherm& and isobaric.) Raloh J. Tvkodi has oosed us the "AG" oroblem for the ~ a ~ - i u s s akxperiment, c and this has led'us to a better presentation of what we tried to sav before. We s i m-~ . l write v AGot as AG,,, = AA.,,
+
+ A(Pv)t,t
= AAsuh = AGsuh - A(p%
Here "tot" refers to the entire svstem. " ~ .D.D "to the aDDara.. tus, and ''sub" to the contained gas. In effect, we have diuided AWVj,,. betu.een the aooaratus and the contained substance: = A(P'~, A(PV).,h. This is the vital step; i t can probably be best taken as simply defining A(PV).,,. The remaining argument is straightforward, except that, by invoking the rigidity of the apparatus, we have assumed A(PWbt = AU., = TAS,,, = 0. So for n moles of perfect gas we find AGsuh= nRT ln(V2 Vl)IVl, A(PV),,h = &AT = 0, and AG,,, = -nRT ln(V2 V1)/Vl. The contributions to AGsppfromthe two bulbs are oppositely equal, and AG,. is negative. For the "ether" experiment (I), conducted in the same apparatus, we find AGsuh = 0 and AGbt = -A(PV),,h = -Pv.,V2 < 0. Again AG,,, is negative. However, the change is due not to AGetherbut rather to -A(PV),,h,, = A(PV).,,. This formulation is also effedive if the processes are made reversible: imaeine that the Gav-Lussac aooaratus sends thegas throughan ideal turbine that drivesan.idealdynarno, which does work on thcsurroundings. T o find -us,., = -AG for the work done, it is again n e c e s k to c o n s i d e r h ~ ~ , in , which, in the case of the vaporizing liquid, AG., is the only nonvanishing part. Although our terms "monoharostatic", "isobarostatic". etc.. possibly could be improved upon, the distinctions they embody are essential. "Isobaric" and "isothermal" are w r rectlv and unambiruousl\f defined in the textbooks:. thev. do not properly applGo the.processes discussed here, or to the application of the G i h h and Helmholtz criteria in general,
a(Pvtot
+
+ +
Volume 68
Number 5 May 1991
443
and i t is important to use terms that do apply. Otherwise, there will he no end to confusion in the respects we have addressed earlier [J. Chem. Educ. 1986,63, 935-937; 1988, 65,393-3941. Note added in proof: Further comment has appeared (2,3). Literature Clted 1. This problem is given in the text Physical Chemislr). by Eggern. Gregory, Hslsey,and
Rabinnvitch, Why.1965. 2. Tykodi. R. J. J. C h e m E d u c . 1990.67.383-384. 3. Sehurnak~r,V.: Waser.J. J . C h e m Edue. 1990,67,3%.
Verner Schomaker California Institute of Technology Pasadena, CA 91 125
JGrg Waser University ol Washinglan Seattle, WA 98195
A Discrepancy ol Language To the Editor:
I enjoyed the article "Buoyancy Measurements for Teaching and Research" [1989, 66, 2671. The discrepancy in volumes was quite intriguing, and I spent two days on this paradox. The solution to the discrepancy is actually one of language. When one says that "the buoyant force is determined by the volume of the fluid displaced, the word displaced is not in the past tense, hut rather in the present tense, "being displaced". This becomes clear if we draw two figures. In the first figure
A
HA =H,,A+al A.AH = a1 = Vs = VL = volume of liquid being displaced A.AH = volume of liquid moved above original level, H, = VL = vs
In the second figure
False Clalms-Correclad To the Editor: Though I am not a chemist, I have found many of the pedagogical articles in this Journal quite stimulating, and in several of them I have found ideas applicable to my own teaching of mathematics. I must, however, take strong exception to a number of statements in the article "Viewing Stereo Drawines" " 11989.66.6641. . . . In particular, its authors make the following categoricalhut entirely unsupported-assertions: (1) "A stereo viewer is indispensable to visualize [stereo pairs] correctly." (2) Thoueh "Such stereo airs. . .are designed t o ~ r o v i d ethe correct three-dimensiohal appearance when viewed with a special device,. . .a mirror image of the true object is perceived with unaided eyes." In fact, both these claims are simply false. I t is true that the method of cross-eyed stereopsis "brings in an inherent error", hut the authors seem completely unaware that there is an alternative method of direct viewing-known as "relaxed stereopsis"-that does not suffer from this defect. In that method, the eyes are directed oarallel to one another. as thoueh eazine a t a distant ohiect., while they are focused close on the respective images of the stereo oair. I t takes some ~ r a c t i c eto master this skill. since the combination of p a r d e l viewing and close focu$ing is never required in ordinary situations: nevertheless. a ereat many people have learned to do it, A d the method icroutinelv taught in courses on aerial maD reading. Those of us w h o m e the relaxed method see exactly the same stereo image by direct viewing as we do with a separating card or magnifying device. Moreover, when the left and right images of a stereo pair are reversed (as they will be if viewed with the cross-eyed technique), the perceived stereo image will not be a mirror imaee of the true obiect. hut rather a ~seudoscooicone. in whiEh all front/back~rel&ionshipsare'reversed. i n the case of the double helix. the result will aooear as a reversal of chirality, hut in a &ore complex image, such as a scene of a tree in front of a building, the pseudoscopic image will hecome "very difficult and confusing" indeed, since the tree will appear to he pushed back through the building that is now in the foreground. The tryptych printing technique is of course useful: it enables either type of viewer to see a proper stereo image, and in cases like the helix, i t provides a compact format for viewing both chiral possibilities. In conclusion, it should he noted that some of the commercial software that has been developed for generating stereo molecular oairs "on screen" (for examole. . . ALCHEMY 11) has been de'signed to accommodateeither type of viewing, h i allowine- the user tochoose whether or not to reverse the left/ right images.
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John W. Dawson, Jr. Penn State York 1031 Edgecarnb Avenue York. PA 17403
HA = H d + a l A.AH = ol = V, = VL =volume of liquid being displaced A.AH - a 4 H = volume of liquid moved above original level, H, = vi
These two volumes are not the same, V LZ VL. In the first figure the upper part of the rod must he suhmerged farther to push more liquid above the original level, H,. This is not meant as a criticism, but a clarification. This article was useful. R. Thomas Myers Kent State University Kent, OH 44242
444
Journal of Chemical Education
Money Is the Answerl To the Editor:
I have read the recent litany of educational system illsand suggested cures ( 1 4 ) with a cynical glee. There is only one real cure for the problems: rnone)!Sure, teachers need to be treated like the professionals they are, given control of their professional lives, and given the &pp&t service8 they need to do the job, hut the key ingredient is a salary competitive with those in the orivate sector. "Eaual Dav for eoual work" is not just a femke demand, i t needsto-he ouis as well.
