similar irreversible deformation occurs wntinuously dming rolling of the unhappy ball, transforming some of the translational kinetic energy into internal energy of the ball. The article goes on to "explain" the relative coefficients of friction of the two materials in terms of chlorine and cyclopentane groups in the molecular structure. However, the relationship between wefficient of friction and molecular structure is tenuous a t best. and often has more to do with the physical condition of t6e surfaces rather than the molecular structure. I n fact. the article mentions that the Norsorex (unhappy material) contains relatively large quantities of a nonvolatile compatible liquid such as highviscosity naphthenic oil, and the presence of this liquid could acwunt for the "internal friction" which slows down the rolling motion. Lois Nicholson Nat onal Research cobncl Office of Sc en! flcand Engmeer ng Researcn Wash ngton. DC 20418
To the Editor: I n the article cited by Nicholson the chemical and physical characteristics of both polychloroprene (neoprene) and polynorbornene (Norsorex) were discussed and the results of the experiments were explained in terms of the contrasting chemical structures of these elastomers. I n several cases, the explanations were oversimplified, and this was arguably appropriate, but unfortuna&ly, in other cases the explanations given were incorrect, a s pointed out in the abbve letter b;~icbolson. The thrust of Nicholson's letter concerns the distinction between surface friction and internal friction. She correctlv points out that rolling balls down a n incline does not meaHu>e relative coefficients of surface friction but some other property. The terminology used in the article is somewhat inexact, which probably prompted Nicholson's letter. Tire adhesion or "grip", rolling resistance, braking, tire wear, etc., are very complex pctiormanre phenomena and are not generally a reflect~onof any one single material properly. However, the rirticlc states that the unhappy ball has a "lugher coefficient of fricuon," and unfi~rtunately the word "coefficient" implie surface friction, when the factor involved here 1s mternal friction or viscous loss, i.e., the so-called rolling resistance, which is a familiar concept within the ruhhrr tire industry. The term'.rollmg friction," is 3 misnomer precisely hecauw it also implies surface friction. Ih~wcvcr,the article is correct in speaking of the henelits of a less resilient (more highly damping, rubber in maintaining road contact. ~ o a d s u ; f a c e s¬ perfect. During cornering or braking, a highly resilient rubber such as natural rubber or cis-polybutadiene will tend to bounce, and the driver can suddenly experience the extremely low coeff~cientof surface friction between rubber and air. The trade-off in switching to a less resilient rubber is increased tire wear and decreased gas mileaee. The article is correct in this proposition, also, since i t warns of excessive heat build-UDand in so doine implies that the friction is internal r a t i e r than surface. Nicholson is also correct in referring to the likely higher trailing edge force for the Norsorex ball during rolling. The Norsorex ball has a lower modulus and deforms substantially more under its own weight than does the neoprene hall. This results not only in greater deformation, leading to higher internal frictional losses, but also results in a larger "footprint" and greater adhesive forces a s the trail-
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868
Journal of Chemical Educat~on
ing - edge - of the contact surface must continually. separate . during rolling. Two incorrect statements in the Conclusions section of the article can be traced to incorrect technical information given to Kauffman et al. by the supplier of the balls (Arbor Scientific), viz., that the glass transition temperature (Tg) of the Norsorex ball is very low (-60 'C). Differential scanning calorimetm, however, revealed that the Norsorex ball (which is a compounded elastomer containing a nonvolat i e plasticizer) &splayed two transitions: a Htrong, very broad transition a t -30 T and a much weaker, relatively sham transition a t 12 'C. indicatine that it is not completely homogeneous, but consists of two phases, one (low T. ohase) relativelv richer in ~lasticizerthan the other (hiih Tgphase). ~ h ; s , rather th'an possessing a glass transition t e m ~ e r a t u r ethat has been lowered "bv almost 100 'C" and r e k n i n g "considerable freedom of roiation [of the chains] a t temperatures a s low a s -60 'C" (p 199), the Norsorex ball, a s shown conclusively by our DSC results, has a two-phase morphology, one phase of which is totally glassy a t 12 C and lower, and the other a t -30 T and lower. The authors wish to thank Robert F Ohm, Technical Director. Rubber Chemicals & Minerals. R. T. Vanderb~ltCo.. Inc., ~ o n v a l k CT , 06855, and ~ n d r dMarbach, ~ a n a g e r ; Norsorex, Atochem, Paris, France, for technical information.
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Robson F. Storey and Raymond B. Seymour University of Southern Mississippi Hattiesburg, MS 39440 George B. Kauffman California State University, Fresno Fresno, CA 93740 Can a Carnot Cycle Ever Be Totally Reversible? To the Editor: I n the paper on the efficiency of reversible heat engines by Seidman and Michalik [J. Chem. Educ. 1991,68, 20% 2101 it is stated that "Atkins makes just such a mistake when he asserts that a reversible Stirline - cvcle " has the same efficiency a s that of a Carnot cycle operating between the same temperatures." Then there follows a n analysis of a three stage reversible cycle and'the Stirling cycle. The writer has found statements similar to the corollary to Carnot's theorem in a t least five engineering thermodynamics books. Also one will find in other books expressions for the thermodynamic efficiency which are not of the Carnot form. The apparent dilemma results from the fact that in general a regenerator, used to achieve the isochoric processes labelled staws 2 and 4 in the Seidman and Michalik paper, is not reveriible so that the Stirling cycle consists of a n irreversible device operating between two isothermal reservoirs and, therefore, must necessarily have a n efficiency lower than Carnot. However, a totally reversible regenerator used in a Stirling cycle must result in a n overall Carnot cycle effkiency so that Atkins' statement is correct a s a n ideal limiting case. What assumption begs the question is whether a regenerator or even a Carnot cycle can ever be totally reversible. The writer believes that the Curzon and Ahlborn [Amel: J. Phys. 1975,43,22-241 concept should replace the standard Carnot analysis. Peter E. Liley Department of Mechanical Engineering Purdue University West Lafayene, IN 47907-1288
