Stokes's Theorem and the Second Law (Errata) To the Editor:
I wish to note two errors in my paper "Stokes's Theorem and the Geometric Basis for the Second Law of Thermodynamics" [1988,65,50-521. The first is a misstatement regarding the gradient vector operator immediately following its definition (eq 3, p 50): "where it is noted that v points in the same direction as r" should read "where this operator has direction onlv when a o ~ l i e dto a function F and V F is nerpendicular ta' surfaceof constant F. In the following discussion it is assumed that Fdepends only on the magnitude of r and not its orientation. Thus, surfaces of constant F are spheres and V F points in the same direction as r." At the top of p 52 it is stated that B can he reoriented to the new vector A "by dividing by a scalar factor X(x,v.z)". However, a scalar cannot change t h e orientation of a Veitor (except by 180°). The variable required to reorient B as shown in Figures 4 and 6 is a tensor, not a scalar. If A is the gradient of a function and B is not but can be converted to A by a scalar, then B and A must both point along the same line. The way this occurs is best seen with ageometric example. The two-dimensional vectors B' = xyi x2j and B = x2i xyj can both be scaled by X = x to give an A which is the gradient of a function. However, A' = y i xj would not give afunction of the proper geometry, while A = x i y j would: F * (x2 y2)/2; V X A = 0, but V X B = yk. Reversible paths along constant F would have both B.dr and A.dr = 0, just as reversible paths with d S = 0 have dQ = 0. A path corresponding to dQ = 0 and d S positive is one from x = 0, y = yl to x = 0. v = v? where -v-l > ". v,. Fieure 6 is incorrect for this s i t u a t i o n ~ h o ~ e ~the e r ,reason B-dr = 0 is that B is zero, not that B is uer~endicularto dr. The cvclic internal of B.dr. $B.dr =-$-(x2dx xydy), along generalbath will of course vary depending on the value of x when y changes, while $A.dr = 0 for any path, according to Stokes's theorem. I thank R. L. Rabie, Los Alamos National Laboratory, for pointing out both these errors to me and R. C. Dunbar, Case Western Reserve University for also indicating the misstatement regarding v.
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member, offhand, the meanings of "atto" or "tera" or "petam?Why bother to remember them? Instead of urging the adoption of more prefixes, there is good reason to propose that some of them should be eliminated. The assertion that the proposed prefix would be convenient is not documented; convenient for whom? No advantage that I can see may he realized by describingamagnitude of length as "1 angstrometer" instead of "0.1 nanometer" or ''lO-'O m". On the contrary, the meaning of the last designation is self-evident. without recourse to orefixes that are arbitrary, esoteric, and unnecessary. There must be a hetter way of honoring the achievements of Anders h g s t r ~ m In . the words of the medieval scholar Evaristo Basta: "Hexadecim satis superque". George Gorln Oklahoma State Univemity Stillwater, OK 74078
An Alternate Use of Dlllthlum Crystals To the Editor:
The Star Trek article by R. L. Hudson [1987,12, 10391 reminded me of an alternate educational use of "dilithium crystals" that I have used many times in explaining the mass-to-energy conversion important in nuclear reactions. I t is proposed that the dilithium fuel is composed of the less abundant (7.42%) Li-6 isotope, and that the starship's power plant is capable of converting this dilithium to C-12: The mass chanee for this reaction is 12.00000 -21fi.015121 - , - - -- = -0.03024 am~.-WhenEinstein's relation is used, the enelgy released is calculated to be 2.72 X lo9 kJ/mol. (This nuclear fusion is more than 50 million times more exothermic than the thermochemical process proposed by Hudson and perhaps more likely given the starship's limited space and extended missions.) Like Hudson, I have found very few students who are unfamiliar with the Enterprise and its fuel.
Lawrence H. Bowen
Frank T. Lang
Norih Carolina State University Raleigh, NC 27695
Feirlelgh Dickinson University Madison, NJ 07940
Please, No Angstrometerl To the Editor:
Schieber and Longo's proposal 11987,64,10301 to establish an additional SI multiplicative prefix, called "angstro" and equal to the factor 10-lo, is indeed provocative. But is i t a good idea? Not in my opinion. At present, 16 such prefixes have been adopted for use in the SI. Some of them are used frequently, and it is an undeniable convenience to have such composite names as kilometer and milligram and microampere. But there is a limit to the number of prefixes that one may reasonably be expected to recognize. How many of us re-
An Omlsslon To the Editor:
Martin M. Anderson's article [1987, 64, 10231 illustrates two working models for the S Nmechanism. ~ Unfortunately, no reference is made to the article Melvin S, Newman of this Department [1975, 52, 4641 12 years which details a more sophisticated model for the same process. Although different in design, the mechanical aspects of the two models are quite similar. Robert J. Ouelletle The Ohio State University 120 West 18th Avenue Columbus. OH 43210
Volume 67
Number 3
March 1990
277
