When we walk down a street in summer, the open windows on the upper floors appear black. Light entering the window scatters on the interior before it finds a way out, by which time it is in thermal equilibrium with the room. Electromagnetic radiation at room temperature is mostly in the infrared part of the spectrum, which is why we see it as black. One can reproduce this arrangement in a laboratory, by drilling a small hole in a polished metal box and measuring the radiant energy emitted by the hole as a function of frequency and temperature, the so-called blackbody radiation. Based on earlier measurements by Dulong and Petit, Josef Stefan postulated the correct equation of state for it empirically. Ludwig Boltzmann later established theoretically that the energy density is proportional to the fourth power of the temperature, but attempts to calculate the constant ran into a serious problem, that the value appeared to be infinite, a result known as the Rayleigh-Jeans ultraviolet catastrophe. Using the formalism developed so far, we first give a short technical derivation of this equation of state, and then discuss the physics at length.

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Light

  • Denis Sunko

摘要

When we walk down a street in summer, the open windows on the upper floors appear black. Light entering the window scatters on the interior before it finds a way out, by which time it is in thermal equilibrium with the room. Electromagnetic radiation at room temperature is mostly in the infrared part of the spectrum, which is why we see it as black. One can reproduce this arrangement in a laboratory, by drilling a small hole in a polished metal box and measuring the radiant energy emitted by the hole as a function of frequency and temperature, the so-called blackbody radiation. Based on earlier measurements by Dulong and Petit, Josef Stefan postulated the correct equation of state for it empirically. Ludwig Boltzmann later established theoretically that the energy density is proportional to the fourth power of the temperature, but attempts to calculate the constant ran into a serious problem, that the value appeared to be infinite, a result known as the Rayleigh-Jeans ultraviolet catastrophe. Using the formalism developed so far, we first give a short technical derivation of this equation of state, and then discuss the physics at length.