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Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment

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Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment Mark P. Silverman and Christopher R. Silverman he rate at which an object cools down Our curiosity was aroused. How good an Tgives valuable information about the approximation to reality is Newton’s law— mechanisms of heat loss and the thermal prop- and what in any event determines whether the erties of the material. In general, heat loss temperature of the hot object is too high? occurs by one or more of the following four Furthermore, although Newton’s name is processes: (a) conduction, (b) convection, (c) readily associated with his laws of motion, evaporation, and (d) radiation. law of gravity, and various optical phenomena In conduction, heat is transferred through a and apparatus, it does not usually appear in medium by the collisional encounters of ther- discussions of thermal phenomena. Indeed, mally excited molecules vibrating about their apart from this one instance, a search through equilibrium positions, or, in the case of met- a score or more of history of science books als, by mobile, unbound electrons; only ener- and thermal physics books at various levels of gy, not bulk matter itself, moves through the instruction produced but one other circum- Mark P. Silverman is material. Convection, by contrast, refers to the stance for noting Newton’s name—and that Professor of Physics at Trinity College and former transfer of heat through the action of a moving was his failure to recognize the adiabatic 3 Joliot Professor of Physics fluid; in free or natural convection, the motion nature of sound propagation in air. This his- at the Ecole Supérieure de is principally the result of gravity acting on torical footnote accentuates, however, the cir- Physique et Chimie (Paris). density differences resulting from fluid cumstance that Newton pursued his interests Among his current research expansion. Evaporation entails the loss of at a time long before the concept of heat was interests are electron inter- heat as a consequence of loss of mass, the understood. He died in 1727, but the begin- ferometry, light scattering in faster-than-average molecules escaping from ning of a coherent system of thermal physics turbid media, and the the free surface of a hot object, thereby might arbitrarily be set at nearly a hundred uncommon physics of com- removing kinetic energy from the system. years later when Sadi Carnot published (1824) mon objects. His most Lastly, radiation involves the conversion of his fundamental studies on “the motive power recent books are Waves the kinetic and potential energy of oscillating of fire” (La puissance motrice du feu). What, and Grains: Reflections on Light and Learning (1998) charged particles (principally atomic elec- then, prompted Newton to study the rate at and Probing the Atom: trons) into electromagnetic waves, ordinarily which hot objects cool, how did he go about Interactions of Coupled in the infrared portion of the spectrum. From it, and where did he record his work? States, Fast Beams, and the perspective of classical physics, charged Loose Electrons (2000), particles moving periodically about their equi- “The heat of a little kitchen fire...” both published by Princeton librium positions (or indeed undergoing any We address the historical questions first. In University Press. kind of acceleration) radiate electromagnetic stark contrast to Newton’s other eponymous Dept. of Physics energy. achievements, for which a physics teacher or Trinity College Although the physical principles behind student desirous of knowing their origins 300 Summit Ave. the four mechanisms lead to different mathe- could turn to such ageless sources as Hartford, CT 06106 matical expressions, it is widely held that, if Principia or Optiks, the paper recording the mark.silverman@ the temperature of a hot object is not too high, law of cooling is decidedly obscure. After mail.trincoll.edu then the decrease in temperature in time fol- much searching, we discovered a reprinting of lows a simple exponential law, an empirical this elusive work in an old (and rather dusty) result historically bearing Newton’s name. As physics sourcebook.4 According to the author, student (CRS) and teacher (MPS) we encoun- William Francis Magie, the paper, “A Scale of tered Newton’s law several times in our the Degrees of Heat,” was published anony- course of study together in both high-school mously in the Philosophical Transactions in math1 and high-school physics.2 1701 although Newton was known to have 82 THE PHYSICS TEACHER Vol. 38, Feb. 2000 Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment written it. (Such a paper is briefly cited—but it at once in a cold place ... and placing with no mention of the law of cooling—in on it little pieces of various metals and Never At Rest, Richard Westfall’s definitive other liquefiable bodies, I noted the biography of Isaac Newton.5) times of cooling until all these bodies Despite its obscurity, this is, like much of lost their fluidity and hardened, and Newton’s work, a fascinating paper. In con- until the heat of the iron became equal trast to what we might expect, Newton’s prin- to the heat of the human body. Then by cipal concern was not to nail down the precise assuming that the excess of the heat of formulation of another physical law, but rather the iron and of the hardening bodies to establish a practical scale for measuring above the heat of the atmosphere, found temperature. By 1701, Newton, then about 60 by the thermometer, were in geometri- years old, had long since completed the fun- cal progression when the times were in damental studies of his youth—motion, grav- arithmetical progression, all the heats ity, the calculus, spectral decomposition of were determined.... The heats so found light, diffraction of light, and much else—to had the same ratio to one another as take up the job of a British functionary. In those found by the thermometer. 1695 he had been appointed Warden of the Mint, and moved from Cambridge to London. And thus Newton’s law of cooling first saw It seems reasonable to us to speculate that light of day. Newton’s concern with temperature and the In fact, that small section above is all that melting points of metals was motivated by his Newton had to say about “Newton’s law.” responsibility for overseeing the purity of the Note that not once in the entire article does national coinage. Newton mention the word “temperature.” At Chris Silverman received a All the same, the experiment was vintage this time the concepts of heat and temperature home-schooled education Newton: clever use of the simplest materials were poorly understood and confounded; (where “home” has included at hand to carry out a measurement of broad Newton refers to both as “heat” (calor in New Zealand, Japan, significance.6 Having selected linseed oil— Latin). Note, too, that nowhere does Newton France, Finland and various which has a relatively high boiling point mention the word “exponential” or give the points in-between). An artist, (289 ЊC) for an organic material—as his ther- equation of exponential form whose drawings have been mometric substance, Newton presumed that displayed in a number of the expansion of the oil was linearly propor- T–T = (T – T )e–kt (1a) solo exhibitions, and a pub- 0 m 0 lished poet, Chris is tional to the change in temperature. With this presently a first-year student thermometer and a chunk of iron heated by with rate constant k, ambient temperature T0 at Trinity College concen- the “coals in a little kitchen fire,” Newton pro- and maximum temperature Tm) that explicitly trating in studio arts and ceeded to establish what quite possibly was shows the temporal variation synonymous computer science. He the first temperature scale by which useful with Newton’s law. However, in verifying the designed the cover of a measurements were made. He set 0 on his points of his scale, Newton asserted that “the book published by Princeton scale to be “the heat of air in winter at which heat which the hot iron communicates in a University Press and is cur- water begins to freeze” and defined 12 to be given time to cold bodies...is proportional to rently working on illustra- “the greatest heat which a thermometer takes the whole heat of the iron”—or, as we would tions for a children’s book. up when in contact with the human body.” On express mathematically in current symbolism Chris has been an avid this fixed two-point scale the “heat of martial artist since he was 10 years old. iron...which is shining as much as it can” reg- d T / dt = –k(T – T ) (1b) 0 Trinity College istered the value 192. 300 Summit St. Having established the above points, as Equation (1a) is the solution to Eq. (1b), and Hartford, CT 06106 well as other intermediate values (e.g., 17: from (1a) the reader will readily confirm that “The greatest heat of a bath which one can endure for some time when the hand is dipped T1 – T0 T2 – T0 T3 – T0 in it and is kept still”7), Newton sought an ᎏᎏ = ᎏᎏ = ᎏᎏ = ... = ek⌬t (1c) independent procedure for confirming their T2 – T0 T3 – T0 T4 – T0 validity. To do this, where the temperatures T1, T2, T3, ... are all ⌬ ... I heated a large enough block of measured at equal intervals of time (t1 = t, t2 ⌬ ⌬ iron until it was glowing, and taking it = 2 t, t3 = 3 t...). This is the “geometrical from the fire with a forceps ... I placed progression” of temperatures (above the Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment Vol.
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