Max Planck - The Theory of Heat Radiation

Among general papers treating of the application of the theory of quanta to different parts of physics are:

1. A . Sommerfeld, Das Plancksche Wirkungsquantum und seine allgemeine Bedeutung fr die Molekularphysik, Phys. Zeitschr., , p. 1057. Report to the Versammlung Deutscher Naturforscher und Aerzte. Deals especially with applications to the theory of specific heats and to the photoelectric effect. Numerous references are quoted.

2. Meeting of the British Association, Sept., 1913. See Nature, , p. 305, Nov. 6, 1913, and Phys. Zeitschr., , p. 1297. Among the principal speakers were J. H. Jeans and H. A. Lorentz. (Also American Phys. Soc., Chicago Meeting, 1913.)

3 . R. A. Millikan, Atomic Theories of Radiation, Science, , p. 119, Jan. 24, 1913. A non-mathematical discussion.

4. W. Wien, Neuere Probleme der Theoretischen Physik, 1913. (Wiens Columbia Lectures, in German.) This is perhaps the most complete review of the entire theory of quanta.

H. A. Lorentz, Alte und Neue Probleme der Physik, Phys. Zeitschr., , p. 1234. Address to the Versammlung Deutscher Naturforscher und Aerzte, Knigsberg, 1910, contains also some discussion of the theory of quanta.

Among the papers on radiation are:

E. Bauer, Sur la thorie du rayonnement, Comptes Rendus, , p. 1466. Adheres to the quantum theory in the original form, namely, that emission and absorption both take place in a discontinuous manner.

E. Buckingham, Calculation of c2 in Plancks equation, Bull. Bur. Stand. , p. 393.

E. Buckingham, On Wiens Displacement Law, Bull. Bur. Stand. , p. 543. Contains a very simple and clear proof of the displacement law.

P. Ehrenfest, Strahlungshypothesen, Ann. d. Phys., , p. 91.

A. Joff, Theorie der Strahlung, Ann. d. Phys., , p. 534.

Discussions of the method of derivation of the radiation formula are given in many papers on the subject. In addition to those quoted elsewhere may be mentioned:

C. Benedicks, Ueber die Herleitung von Plancks Energieverteilungsgesetz, Ann. d. Phys., , p. 133. Derives Plancks law without the help of the quantum theory. The law of equipartition of energy is avoided by the assumption that solids are not always monatomic, but that, with decreasing temperature, the atoms form atomic complexes, thus changing the number of degrees of freedom. The equipartition principle applies only to the free atoms.

P. Debye, Plancks Strahlungsformel, Ann. d. Phys., , p. 1427. This method is fully discussed by Wien (see 4, above). It somewhat resembles Jeans method (Sec. 169) since it avoids all reference to resonators of any particular kind and merely establishes the most probable energy distribution. It differs, however, from Jeans method by the assumption of discrete energy quanta h . The physical nature of these units is not discussed at all and it is also left undecided whether it is a property of matter or of the ether or perhaps a property of the energy exchange between matter and the ether that causes their existence. (Compare also some remarks of Lorentz in .)

P. Frank, Zur Ableitung der Planckschen Strahlungsformel, Phys. Zeitschr., , p. 506.

L. Natanson, Statistische Theorie der Strahlung, Phys. Zeitschr., , p. 659.

W. Nernst, Zur Theorie der Specifischen Wrme und ber die Anwendung, der Lehre von den Energiequanten auf Physikalischchemische Fragen berhaupt, Zeitschr. f. Elektochemie, , p. 265.

The experimental facts on which the recent theories of specific heat (quantum theories) rely, were discovered by W. Nernst and his fellow workers. The results are published in a large number of papers that have appeared in different periodicals. See, e.g., W. Nernst, Der Energieinhalt fester Substanzen, Ann. d. Phys., , p. 395, where also numerous other papers are quoted. (See also references given in 1.) These experimental facts give very strong support to the heat theorem of Nernst (Sec. 120), according to which the entropy approaches a definite limit (perhaps the value zero, see Plancks Thermodynamics, 3. ed., sec. , et seq.) at the absolute zero of temperature, and which is consistent with the quantum theory. This work is in close connection with the recent attempts to develop an equation of state applicable to the solid state of matter. In addition to the papers by Nernst and his school there may be mentioned: