Müller I. A history of thermodynamics. The doctrine of energy and entropy (1185104), страница 47
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Joseph von Fraunhofer (1787–1826)addressed those difficulties. He was an optician with strong scientificinterests and he became an expert in making achromatic lenses. Also thequality of his prisms allowed him to discover lacking frequencies, i.e. darklines in the spectra of the sun and of stars, – several hundred of them.Fraunhofer’s optical instruments served Bessel to discover the parallax ofsome stars, and therefore his gravestone carries the euphemistic engravingin Latin: Approximavit sidera – he brought the stars closer.
Well, at least hedid help to make astronomers appreciate how far away the stars really were.However, the significance of the dark lines was not recognized byFraunhofer, or anybody else in Fraunhofer’s time.The study of hot gases and the light which they emit became a popularand important field of research in the mid 19th century and Gustaf RobertKirchhoff (1824–1887) was the most conspicuous researcher in that field.He worked with Robert Wilhelm Bunsen (1811–1899), the inventor of theBunsen burner, which burns with the emission of so little light thateverything burning in it can be clearly distinguished.
Kirchhoff discoveredthat each element, when heated to incandescence, sends out light offrequencies that are characteristic for the element. Thus with hisspectroscope he discovered several new elements, e.g. cesium andrubidium, both named – in Latin – for the colour of their spectral lines: blueand red respectively.Moreover, Kirchhoff found that when light passes through a thin layer ofan element – or through its vapour – it would lose exactly those frequencieswhich the hot element emits. That observation is sometimes calledKirchhoff’s law, enunciated in 1860. So, since the sunlight lacks thefrequencies that heated sodium (say) emits, Kirchhoff concluded thatsodium vapour must be present at the solar surface. This was considered agreat feat, since it gave evidence of the composition of the sun, somethingwhich had been deemed impossible before.
Asimov writes11I. Asimov: “Biographies ...” loc.cit. p. 377.Black Bodies and Cavity Radiation199Thus was blasted the categorical statement of the French philosopherAuguste Comte who, in 1835, had declared the composition of the stars tobe an example of the kind of information science would be eternallyincapable of obtaining. Comte died (insane) two years too soon to seespectroscopy developed.Kirchhoff conceived of a black body, a hypothetical body that sends outradiation of all frequencies and that should therefore – by Kirchhoff’s law –also absorb all radiation, and reflect none, so that it appears black.
Suchblack bodies came to play an important role in radiation research, althoughin the early days no real good black body existed to serve as a reliableobject of study. Therefore Kirchhoff suggested an ingenious surrogate inthe form of a cavity with blackened, e.g. soot-covered interior walls, whichcould be heated. Any radiation that enters the cavity by a small hole isabsorbed or reflected when it hits a wall. If reflected, the light will mostlikely travel to another spot of the wall, being absorbed or reflected there,etc. etc. In this way virtually no reflected light comes out through the holeso that the hole itself absorbs radiation as if it were a black body.
Theradiation emitted through the hole is called cavity radiation and it can bestudied at leisure for any temperature of the walls.Kirchhoff himself found that the energy flux density JȞdȞ emitted by a blackbody, or a cavity between frequencies Ȟ and Ȟ + dȞ depends on thetemperature of the body universally, i.e. it is independent of the mechanical,or electrical, or magnetic properties of the body. 2 Thus Kirchhoff focusedthe interest of physicists on the universal function JȞ(Ȟ,T), the spectralenergy flux density.Of course, at that time it was already well-known that there is more toradiation than can be seen. As early as 1800 the eminent astronomerFriedrich Wilhelm Herschel, – Sir William since 1816, the discoverer ofthe planet Uranus – had placed a thermometer below the red end of the solarspectrum and noticed that it registered a fast increasing temperature. Thushe discovered heat radiation which came to be called infrared radiation.And then Johann Wilhelm Ritter (1776–1810), an apothecary, discovered in1801 that silver chloride, which was known to break down under light –changing colour from white to black, the key to photography – continued todo so, if placed beyond the blue and violet end of the spectrum.
In thismanner he detected ultraviolet radiation.2It is always difficult to prove experimentally that some property of bodies is universal,because one would have to test all existing bodies. However, in Kirchhoff’s timeprogressive scientists knew the then new second law very well and its universal prohibitionthat heat pass from cold to hot.
So Kirchhoff used a cumbersome thought experiment toprove that, if JȞ(Ȟ,T) were dependent on material, the second law could be contradicted.The argument is convincing enough, but somewhat boring; therefore I skip it. The same istrue for some arguments by Wien, see below.200 7 Radiation ThermodynamicsIn 1879 Josef Stefan (1835–1893), Boltzmann’s mentor in Vienna foundby careful experimentation that the radiant energy flux densityJf³ J Q dQ0emanating from a black body – as black as possible – was proportional tothe fourth power of its absolute temperature.
Thus a body of 600K emitssixteen times more energy than at 300K. Stefan’s experiments also provideda rough value for the factor of proportionality which, of course, is universal,since JȞ(Ȟ,T) is universal.Kirchhoff’s cavity-model was much more than a means of obtaininggood-quality black body radiation.
It proved to be an important heuristictool for theoretical studies. One feature that attracted physicists to theradiation-filled cavity was its similarity to a cylinder filled with a gas. Thesimilarity becomes even more pronounced when one wall of the cavity isconsidered a movable piston, thus making it possible to apply work to theradiation, or to extract work from it – at least in imagination. Moreover, theenergy density e of the cavity radiation can easily be measured, becausee = 4/c J holds, where J – as before – is the measurable energy flux densityemitted by the hole in the cavity wall.Fig.
7.1. Gustav Robert Kirchhoff (1824–1887) a pioneer of electrical engineering and ofradiation thermodyanmics. Kirchhoff is best known for the Kirchhoff rules about currentsand voltage drops in electric circuitsBoltzmann utilized the cavity model in 1884 to corroborate Stefan’sT4-law: With considerable courage – or deep insight – he wrote a Gibbsequation for the radiation in the cavity in the formdS1[d ( eV ) pdV ] .TNow, Boltzmann was also an eager student of Maxwell’s electromagnetism and so he knew that the radiation pressure p and the energydensity e of radiation are related so that p = 1/3e holds, see Chap. 2.Therefore the integrability condition implied by the Gibbs equation readsViolet Catastrophe201dlne = 4·dlnT so that e must be proportional to T4 just as Stefan had found itto be.
The T4-law has been called the Stefan-Boltzmann law ever since.And this was just the beginning of the scientific return – experimental orconceptual – from the cavities. Experimentalists used them to measure thegraph JȞ(Ȟ,T), cf. Fig. 7.2 and theoreticians used them to derive the functionthat fitted the graph.Fig. 7.2. Wilhelm Wien (1864–1928). Spectral energy density of black body radiation asobserved (not the Wien ansatz!).
For small values of Ȟ the graphs are parabolicOne of the experimentalists was Wilhelm Wien (1864–1928): He foundthat the peak of the graph shifts to larger frequencies in a mannerproportional to T,3 and he fitted a function of the type4J Q (Q , T )BQ 3 e hkTQ( Wien´s ansatz )to the descending branch of JȞ(Ȟ,T) for large frequencies.5 B and h areconstants, universal ones of course, since the whole function is universal.The opposite limit for small frequencies deserves its own section, sinceits explanation baffled the scientists in the 1890’s.Violet CatastropheWhile actual cavities had soot-blackened walls for practical purposes,theoreticians did not see why the walls should not be perfectly reflecting inmost parts, as long as they contained a tiny black spot of temperature T.
The345This observation became known as Wien’s displacement law.Of course Wien did nor write h, he combined h/k into a universal constant Į. Wien’s ansatzis not altogether too bad: It satisfies the T 4-law and Wien’s own displacement law.However, the Ȟ3-dependence for small frequencies was contradicted by experiments. Thecurves should start with Ȟ2.W. Wien: Wiedemann’s Annalen 58 (1896) p. 662.202 7 Radiation Thermodynamicseffect on the cavity radiation should be the same, at least if the hole wassmall enough; after all, the radiation is universal, independent of the natureof the wall.
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