A Brief History of the T4 Radiation Law

Since the 1700s, natural philosophers understood that heat exchange between two bodies was not precisely linearly dependent on the temperature difference, and that at high temperatures the discrepancy became greater. Over the years, many models were developed with varying degrees of success. The lack of success was due to the difficulty obtaining accurate experimental data, and a lack of knowledge of the fundamental mechanisms underlying radiation heat exchange. Josef Stefan, of the University of Vienna, compiled data taken by a number of researchers who used various methods to obtain their data, and in 1879 proposed a unique relation to model the dependence of radiative heat exchange on the temperature: the T law. Stefan’s model was met with some skepticism and was not widely accepted by his colleagues. His former student, Ludwig Boltzmann, who by then had taken a position at the University of Graz in Austria, felt that there was some truth to the empirical model proposed by his mentor. Boltzmann proceeded to show in 1884, treating electromagnetic radiation as the working fluid in a Carnot cycle, that in fact the T law was correct. By the time that Boltzmann published his thermodynamic derivation of the radiation law, physicists became interested in the fundamental nature of electromagnetic radiation and its relation to energy, specifically determining the frequency distribution of blackbody radiation. Among this group of investigators was Wilhelm Wien, working at Physikalisch-Technische Reichsanstalt in Charlottenburg, Berlin. He proposed a relation stating that the wavelength at which the maximum amount of radiation was emitted occurred when the product of the wavelength and the temperature was equal to a constant. This became known as Wien’s Displacement Law, which he deduced this by imagining an expanding and contracting cavity, filled with radiation. Later, he combined his Displacement Law with the T law to give a blackbody spectrum which was accurate over some ranges, but diverged in the far infrared. Max Planck, at the University of Berlin, built on Wien’s model but, as Planck himself stated, “the energy of radiation is distributed in a completely irregular manner among the individual partial vibrations...” This “irregular” or discrete treatment of the radiation became the basis for quantum mechanics and a revolution in physics. This paper will present brief biographies of the four pillars of the T radiation law, Stefan, Boltzmann, Wien and Planck, and outline the methodologies used to obtain their results. EARLY RADIATION STUDIES Heat transfer, as a serious branch of study in physics, began with Sir Isaac Newton, although his contributions to this subject are but a small part of his complete body of work including calculus, mechanics, optics, and of course, gravity. Natural philosophers of the day deduced that the heat transfer rate was some function of the temperature, although they had difficulty distinguishing between the now commonly known modes of heat transfer: conduction, convection and radiation. Early research into geological history motivated Joseph Fourier to study heat conduction in solids, and then extend his work to incompressible fluids, but postponed any kind of work studying heat transfer in atmospheric gases. Early visual studies of convection heat transfer in gases were performed by Rinaldini in 1657. Euler began the first mathematical theories of convection, and Rumford later discovered convection currents in liquids in 1797. At the time, scientists had difficulty separating conduction and convection in a fluid, and it was widely held that fluids did not conduct heat. Early researchers had a rudimentary knowledge of radiation heat transfer, and believed that heat could be