Temperature and Entropy of Radiation

Wesendonck, K. (1899). Zur thermodynamik. Ann. Phys. 305 (12), 832:

Strahlungsenergie ist eben nicht Wärme und nur in übertragener Bedeutung ist hier von Temperatur sprechen.

Wien, Nobel Lecture, 1911:

The Kirchhoff theorem is not limited to radiation caused by thermal processes. It seems to be valid for most, if not all luminous processes. That the temperature concept can be applied to all luminous processes is beyond doubt. Since we can produce all types of light by means of hot bodies, we can ascribe, to the radiation in thermal equilibrium with hot bodies, the temperature of these bodies, and thus every radiation, even that issueing from a phosphorescent body, has a certain temperature for every colour. This temperature has however no connection whatever with that of the body, nor is it possible as yet to state how e.g. a phosphorescent body comes into equilibrium with radiation. These conditions are bound to be very complicated, in particular in the case of bodies which convert the absorbed radiation and emit it after a long interval of time.

Clear conflation of thermal equilibrium with radiation equilibrium!

Konen and Jungjohann, Studies on the Emission of Gases, p. 416, 1910:

It is assumed by many that with constant pressure temperature is the controlling variable… The mean internal energy is supposed to depend on the temperature of the centers of radiation, and upon these again depends the energy of the radiation. Whether the inner energy of the radiating parts sustains a simple relation with the temperature in an ordinary sense remains uncertain. But in any case, it seems possible that this may be so, and, further, that there exists a simple relation between the internal energy and the radiated energy; in form, this relation may agree with similar laws of a black body. Chemical processes and ionization are then regarded as also determined by the temperature. But the temperature of the luminous centers in question, which possibly constitute but a small fraction of the gas, is not directly measurable, since all measurements furnish only a mean value. Therefore, even if we adopt the above point of view, we may not employ the temperature of luminosity as a variable; the converse process only can be employed. We may measure the change of energy in a spectral system (e.g. a series) and from the change, on the basis of some definite hypothesis, such as the assumption that the rules hold good as for a black body, compute a temperature, the validity of which may be tested in some other way. This procedure was first carried out in a logical manner by Kayser.

9. A modification of the view given here is to regard the temperature as the variable in the ordinary sense, at least in many cases. The temperature of luminosity of a radiating gas would then be defined as that temperature at which a black body is in radiation equilibrium with the gas in question… noteworthy results have been obtained on this assumption.

'Radiation equilibrium' != thermal equilibrum?

Planck, The Theory of Heat Radiation, 1911, p. 16:

A finite amount of radiation always contains a finite although possibly very narrow range of the spectrum. This implies a fundamental difference from the corresponding phenomena of acoustics, where a finite intensity of sound may correspond to a single definite frequency. This difference is, among other things, the cause of the fact that the second law of thermodynamics has an important bearing on light and heat rays, but not on sound waves.

The last sentence is odd given that Planck believes in the absolute generality of the second law.

V. A. Michelson, as quoted in "The black body and the measurement of extreme temperatures" by A. L. Day:

But with the formulation of this law (Wien's), as given by the author himself and accepted, among others, by Planck, I do not entirely agree.

The point at issue is this, that Wien affirms that completely unordered (black) radiation consists of innumerable multitudes of different monochromatic radiations which, he says, are merely mixed mechanically and possess each its own individual energy; on varying the temperature, each by itself follows the law of Stefan, and besides, according to the "displacement law," changes its wave-length, X, in inverse proportion to the absolute temperature. The condition of thermal (radiational) equilibrium W. Wien and Planck find in the identical temperatures attributed to all elementary monochromatic radiations. But to assert this is, in my opinion, to carry too far the analogy between black radiation and a mixture of a multitude of different gases.

In the first place, to speak of "temperature" of monochromatic radiation is possible only very conditionally and with reservations, because such radiation cannot be in thermal equilibrium with any actually hot body. In the second place, I hold it as certain that, in black radiation, the different monochromatic constituent parts of it have not each its own individual existence, but continually mingle their energies. If such an uninterrupted exchange of energy does not take place among the different radiations, I do not see how we can rationally explain the Kirchhoff function $e_\lambda$ as synonymous with the dynamic stability of completely unordered radiation… In this respect, the diffuse radiation inclosed in an opaque envelope differs essentially from the radiation which is freely propagated in the ether. Here a determined period of oscillation is indissolubly connected with every element of energy, and the latter is completely characterized by just that period, together with a particular amplitude and azimuth of polarization. Upon removal of the source, and upon passing through the different centers, the amplitude and polarization may change; the period alone (except under a few rare conditions) remains unchanged. It then brings us information even from the different stellar worlds which give spectra of thin lines. But in the diffuse radiation of a black body there are no traces of any lines, there are no indissoluble ties connecting the period with the individual portions of radiant… energy Just as the heat equilibrium of gas, characterized by the law of Maxwell, is only maintained, because of the uninterrupted exchange of velocity among the different molecules of the gas, so also the law of Kirchhoff is verified by the uninterrupted exchange of energy between oscillations of different periods.

Michelson here is adhering to a strict definition of temperature as defined by being in thermal equilibrium with another body of the same temperature. Wien however likely thinks of himself as extending the definition of temperature.

"The black body and the measurement of extreme temperatures" by A. L. Day, pp. 30-1:

The radiation from the sun is certainly not pure temperature radiation, but partakes of the character of luminescence, between which and the black body no temperature relation has ever been found.

Wilhelm Wien, in Lord Kelvin. Annalen der Physik, 330: 1–6.:

Die Verallgemeinerung des Temperaturbegriffs auf die vollständig von der Materie losgelöste Strahlung wollte er nicht anerkennen.

Wien to Lorentz, 1907:

Was Ihre Bemerkung betrifft, dass ein Lichtbündel durch Wellenlänge und Intensität vollkommen bestimmt sein muss, so bin ich auch dieser Meinung, ich glaube aber kaum, dass man sie allgemein für selbstverständlich halten wird. Jedenfalls scheint doch vielfach die Meinung zu herrschen, dass der Begriff der Temperatur und Entropie auf Vorgänge, die nicht durch Wärme hervorgerufen werden, wie die Strahlung Geisslerscher Röhren, nicht anwendbar sei.

Planck to Lorentz, 1909:

Ich halte es für unmöglich, Temperatur, Entropie, Wahrscheinlichkeit für eine reine Hohlraumstrahlung auch nur zu definiren, ohne Berücksichtigung der Wirkung dieser Strahlung auf emittirende und absorbirende Teilchen. Dieser Punkt ist mir äusserst wichtig, und ich würde Ihnen zu grossem Danke verbunden sein, wenn Sie mir Gegengründe gegen meine Meinung anführen wollen. Denn gerade hierin erblicke ich den wichtigsten Unterschied zwischen den Vorgängen bei der Wärmestrahlung und den Vorgängen bei den Molekularbewegungen. Die Strahlungsvorgänge in einem vollständig evacuirten von spiegelnden Wänden umgebenen Hohlraum sind nach meiner Meinung alle reversibel, Wahrscheinlichkeitsbetrachtungen sind unnötig und unzulässig, jedes Strahlenbündel pflanzt sich mit constanter Helligkeit unabhängig von allen andern fort. Bei den Molekularbewegungen kann man nicht einmal für ein (unendlich) kleines Zeitelement die Richtung des Vorganges angeben, ohne Wahrscheinlichkeitsbetrachtungen anzustellen; denn die Resultate der Zusammenstösse lassen sich nicht eindeutig angeben. Würden die Moleküle durcheinander hindurchgehen ohne ihre Geschwindigkeiten zu ändern, dann hätten wir auch keine Aenderung der Entropie und keine Annäherung an die stationäre Geschwindigkeitsverteilung.

This is intriguing. Planck is offering a physical reason for molecular disorder, and claiming that it does not exist for radiation. So in fact 'natural radiation' is not completely analogous to molecular disorder. In fact, 'natural radiation' is due to molecular disorder!

Lorentz to Planck, 1909:

I also admit that we cannot speak of entropy of ether in itself and that its value is connected with the properties of matter.

Einstein to Lorentz, 1909:

die Voraussetzung, die Energie der emittierten Elektronen entspreche der Temperatur des einfallenden Strahlenbündels, durch unserere gegenwärtigen theoretischen Auffassungen (Elektromagnetik) nicht gestützt wird