Ht2009-88060

Proceedings HT 2009 2009 ASME Summer Heat Transfer Conference July 19-23, 2009, San Francisco, California USA HT2009-88060 A BRIEF HISTORY OF THE T4 RADIATION LAW John Crepeau University of Idaho Department of Mechanical Engineering PO Box 440902 Moscow, ID 83844-0902 USA ABSTRACT he combined his Displacement Law with the T4 law to give a Since the 1700s, natural philosophers understood that heat blackbody spectrum which was accurate over some ranges, but exchange between two bodies was not precisely linearly diverged in the far infrared. dependent on the temperature difference, and that at high Max Planck, at the University of Berlin, built on temperatures the discrepancy became greater. Over the years, Wien’s model but, as Planck himself stated, “the energy of many models were developed with varying degrees of success. radiation is distributed in a completely irregular manner among The lack of success was due to the difficulty obtaining accurate the individual partial vibrations...” This “irregular” or discrete experimental data, and a lack of knowledge of the fundamental treatment of the radiation became the basis for quantum mechanisms underlying radiation heat exchange. Josef Stefan, mechanics and a revolution in physics. of the University of Vienna, compiled data taken by a number This paper will present brief biographies of the four of researchers who used various methods to obtain their data, pillars of the T4 radiation law, Stefan, Boltzmann, Wien and and in 1879 proposed a unique relation to model the Planck, and outline the methodologies used to obtain their dependence of radiative heat exchange on the temperature: the results. T4 law. Stefan’s model was met with some skepticism and was EARLY RADIATION STUDIES not widely accepted by his colleagues. His former student, Heat transfer, as a serious branch of study in physics, Ludwig Boltzmann, who by then had taken a position at the began with Sir Isaac Newton, although his contributions to this University of Graz in Austria, felt that there was some truth to subject are but a small part of his complete body of work the empirical model proposed by his mentor. Boltzmann including calculus, mechanics, optics, and of course, gravity. proceeded to show in 1884, treating electromagnetic radiation Natural philosophers of the day deduced that the heat transfer as the working fluid in a Carnot cycle, that in fact the T4 law rate was some function of the temperature, although they had was correct. difficulty distinguishing between the now commonly known By the time that Boltzmann published his modes of heat transfer: conduction, convection and radiation. thermodynamic derivation of the radiation law, physicists Early research into geological history motivated Joseph Fourier became interested in the fundamental nature of electromagnetic to study heat conduction in solids, and then extend his work to radiation and its relation to energy, specifically determining the incompressible fluids, but postponed any kind of work studying frequency distribution of blackbody radiation. Among this heat transfer in atmospheric gases. Early visual studies of group of investigators was Wilhelm Wien, working at convection heat transfer in gases were performed by Rinaldini Physikalisch-Technische Reichsanstalt in Charlottenburg, in 1657. Euler began the first mathematical theories of Berlin. He proposed a relation stating that the wavelength at convection, and Rumford later discovered convection currents which the maximum amount of radiation was emitted occurred in liquids in 1797. At the time, scientists had difficulty when the product of the wavelength and the temperature was separating conduction and convection in a fluid, and it was equal to a constant. This became known as Wien’s widely held that fluids did not conduct heat. Displacement Law, which he deduced this by imagining an Early researchers had a rudimentary knowledge of expanding and contracting cavity, filled with radiation. Later, radiation heat transfer, and believed that heat could be 1 Copyright © 2009 by ASME transferred by radiation through a vacuum. To separate Institute of Physics at the University of Vienna, a position he conduction and convection effects from radiation, it would be held until his death in 1893.[9] Among his students at the necessary to draw a vacuum between two surfaces. It was not Institute were Ludwig Boltzmann and the psychoanalyst fully understood, however, that a sufficiently low pressure had Sigmund Freud, who took physics courses as part of his to be achieved and that residual gases could affect the radiation medical studies. transfer by absorption and reradiation. One observation that became quite clear was that at high temperatures, the heat transfer was no longer simply a function of the temperature difference. What the dependence was, however, was another issue. For a more detailed early history of heat transfer, see Brush [1,2]. After some issues in trying to determine a proper temperature scale, and some fits and starts, Dulong and Petit [3] performed a series of experiments to determine the rate of radiation heat transfer between two bodies. Their paper, which was awarded a prize from the French Académie des Sciences in 1818 proposed a relation for the emissive power of radiation, Ea= μ T (1) Where a =1.077 and μ was a constant dependent on the material and size of the body. The dependence on the temperature in the exponent helped explain the higher heat transfer rates at higher temperatures, but had a significant disadvantage. There would be heat transfer even at T = 0. Nevertheless, even decades after the T4 law was discovered, a textbook stated that the Dulong and Petit law, “seems to apply with considerable accuracy through a much wider range of temperature differences than that of Newton,” and is based on “one of the most elaborate series of experiments ever Figure 1. Portrait of Josef Stefan, taken around 1885. conducted.”[4] Further experiments were performed by Tyndall [5], Provostaye and Desains [6], Draper [7] and Ericsson [8], Stefan did not feel comfortable with the Dulong and all making slight variations to the constants determined by Petit law, so he began to delve into their work more closely. Dulong and Petit, but keeping the basic structure of the model Drawing on his past experience in conduction heat transfer, he intact. This was the state-of-the-art when Josef Stefan, reconstructed their apparatus, shown in Fig. 2. Based on the Professor and Director of the Institute of Physics at the design, he estimated that a significant portion of the heat was University of Vienna began his own investigation of the lost by conduction and not by radiation, as had been presumed problem. by Dulong and Petit. By subtracting out the heat lost by conduction and reanalyzing the data, Stefan saw that the heat transfer was proportional to the temperature to the fourth JOSEF STEFAN 4 Josef Stefan (Fig. 1) was born on March 24th, 1835 in power. Figure 3 below shows the form of the T law as it first the small village of St. Peter, on the outskirts of Klagenfurt, in appeared in print in 1879.[10] Stefan didn’t realize the modern-day Austria. He was the illegitimate son of ethnic importance of his proportionality constant, A, but noted that it, Slovenes. His father Aleš was a miller and baker, and his “depend[ed] on the size and the surface of the body.” He also mother Marija Startinik was a maidservant. He began his noted that the temperature had to be given in absolute values. studies at the University of Vienna in 1853, studying physics The unusual form of his model forced Stefan to test it and mathematics, graduating in 1857. The year after his on previously published data, and he wanted to see how well it graduation, he passed his doctoral examination at the worked at temperatures higher than those used by Dulong and University of Vienna and accepted a position at the University’s Petit. He first looked at Tyndall’s work, which gave heat Physiological Institute. He was more interested in physics- transfer data on a platinum wire over a wide temperature range. related work, and was eventually offered a full professorship in After studying Tyndall’s data, Stefan wrote, “From weak red mathematics and physics in 1863, becoming the youngest heat (about 525°C) to complete white heat (about 1200°C) the person in the Austro-Hungarian empire to hold that rank. Two intensity of the radiation increases from 10.4 to 122, thus years later in 1865, he was appointed the Director of the nearly 12-fold (more precisely 11.7). The ratio of the absolute temperature 273+1200 and 273+525 raised to the fourth power 2 Copyright © 2009 by ASME gives 11.6.” [11] This result gave Stefan additional confidence His mother was Maria Pauernfeind, the daughter of a well-to- in his model, and he proceeded to test it on the data of do Salzburg merchant.[12] He was a precocious boy who early Provostaye and Desains, Draper, and Ericsson, and found that in life was taught by a private tutor, and then as the family the T4 model fit their data better than the Dulong and Petit moved to various locations throughout Austria, attended the model. local Gymnasium. He took piano lessons from the famed composer Anton Bruckner. Although the lessons ended abruptly, Boltzmann continued to play the piano for the rest of his life.[13] In 1863, Boltzmann entered the University of Vienna to study mathematics and physics, and after publishing two papers, received his Ph.D. just three years after matriculating. He arrived at the Institute of Physics not long after Stefan assumed the Directorship. Stefan was just nine years older than his student. Also at the Institute was Josef Loschmidt, an older scientist who took Boltzmann under his wing.

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