J. A. Campbell Harvey Mudd College Claremont, California
Is
AS Naught or
Not?, Part Ill
Schottky effect.% The Schottky heat capacity for a system of two nondegenerate energy levels separat,ed T h e publication of the letter from Proby energy A E is given by fessor 1-portne in THIS JOURNAL, 45, 9 (196S), certainly increased the mail input into Claremont (and hence, of course, the entropy.) Now that the replies of the five thermodynamicists have appeared in THIS JOURNAL, 45, 244 (1968) further comments may be expected; where x = (-AE/kT). The entropy increment behut they will probably lead to private communication tween any two temperatures is given by rather than journal pages. In any case, the wealth of possibilities of approach to thermodynamic problems should be apparent. Perhaps a brief summary, in lieu of publishing all the comments would be of inand for our particular case by terest. About half of the replies said that the situation of total population of an upper state could never exist, and that the problem was, therefore, nonsensical. Holyever, in lasers, in nmr spectroscopy, in shock tubes, "The function xeZ/(l eZ)% is "odd" in the sense and in crystal modifications (if you will) such inversions that f(-x) = -f(x). [This can be demonstrated by can occur. Perhaps a quarter of the total responses multiplication of the function by exp (-2x)/exp denied t,hat a reversible path was available and, thus, (-2x).] Since the function is odd, its symmetric said classical thermodynamics was not applicable to the integral about zero must vanish, and A S = 0 in acproblem; but the printed solutions both in April and cord with the statistical formulation A S = k ln (1/1) = here show this is not so. One went so far as to suggest 0." that classical and statistical approaches should not A similar letter from Professor Charles E. Hecht of be m i ~ e d ,a piece of advice I'd personally hat,e to see Hunter College points out he had discussed this prohhold sway. lem in THIS JOURNAL.^ HOWsad it is to find good The last quarter of the responses attacked the probarticles unread! lem through t,he device of negative temperatures I cannot resist an addendum of my own: (1) Too similar to Thermodynamicists I and IV. Professor many professors emphasize classical thermodynamics, Wulff's comments seem especially clear. plus reference to the Boltzmann distribution equation, From Professor Claus A. Wulff, Depart,ment of as giving a sufficient picture of the power of thermoChemistry, University of Vermont: dynamics, (2) too little emphasis is placed on inter"The problem stated in J. CHEM. EDUC.,45, 9 preting the entropy of any system in terms of the en(1968) seems applicable only to a system with a finite tropy of mixing of its component distinguishable states, number of energy levels. If one assumes that the (3) too little use is made of simple statistical ideas particles of the system are in internal equilibrium with as A S = R in (W,/Wl), ideas which students find one another such that the relative populations of the much more useful and applicable than simple adhervarious levels are given by ence to A S = q,,,/T. I also suggest that teachers of thermodynamics n; = no exp ( - AEiIRT) consider, not for adoption, but for inclusion among the (in terms of t,he energy separations from the lowest many other statements of the Third Law, the followstate, A E ~then ) concentration of the particles in the ing. "The entropy of any system of indistinguishable higher energy states can occur only at negative abparticles is zero." solute temperatures.' If the above distribution function is valid only the lowest and highest energy levels can contain all the particles-the former a t +O°K 1 A typical discussion of negative absolute temperatures i~ and the latter at -OoI
