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There were derived many forms of the Planck distribution function (PDF) since its discovery by Planck in 1900 and formulae for the positions of Wien´s peaks in those distributions. There were published many attempts searching for the hidden carriers of heat because the existing known heat effects of photons cannot interpret all observed data. In this presented model we work with concept of fission of one Solar photon into two thermons – the missing carriers of heat. Properties of Solar photons and Solar thermons are compared for the surface of the Sun and in the vicinity of the Earth. Solar thermons obey the Stefan-Boltzmann law and their heat action can be experimentally analyzed in the whole volume of the Solar System. One of those effects can explain the microwave background radiation as the reflection of thermons on the surface of the Termination shock. The measure of the quantity of heat S for thermons is constant in agreement with the Carnot´s model. The specific heat of solids was newly interpreted as the joint action of three types of thermons with frequency ν/2, ν, and 2ν. The ratio of these three thermons can be experimentally determined from infrared spectra of those studied solids. This model could bring a new way to better describe the old, predicted concept of “dark heat” as appeared many times in the historical literature. We have summarized the known forms of the PDF and positions of Wien´s peaks in order to search some hidden properties in those mathematical structures. It will be shown that these very well-known formulae to all scholars might still keep some hidden surprising properties.

References

  1. Wien W. Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. 1893; S. 55. German.
     Google Scholar
  2. Wien W. Űber die Energievertheilung im Emissionspectrum eines schwarzen Körpers. Annalen der Physik und Chemie. 1896; 294(8): 662-669. German.
     Google Scholar
  3. Planck M. Űber eine Verbesserung der Wien´schen Spectralgleichung. Verhandlungen der Deutschen Physikalischen Gesselschaft. 1900; 2: 202-204. German.
     Google Scholar
  4. Einstein A. Űber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik. 1905; 17: 164-181. German.
     Google Scholar
  5. Nernst W. (Editor). Die Theorie der Strahlung und der Quanten. Verhandlungen auf einer von E. Solvay einberufenen Zusammenkunft (30. Oktober bis 3. November 1911). Knapp Verlag, Halle a.S., 1914. German.
     Google Scholar
  6. Kangro H. Vorgeschichte des Plankschen Strahlungsgesetzes. Messungen und Theorien der Spektralen Energieverteilung bis zur Begründung der Quantenhypothese. Franz Steiner Verlag, Wiesbaden, 1970. German.
     Google Scholar
  7. Kuhn TS. Black-body theory and the quantum discontinuity, 1894-1912. The University Chicago Press, 1978.
     Google Scholar
  8. Gershun AA. On the spectral density of radiation. Uspekhi Fizicheskich Nauk. 1952; (3): 388-395. Russian.
     Google Scholar
  9. Foitzik L. Űber die Darstellung der spektkralen Energieverteilung von Strahlungsquellen. Experimentelle Technik der Physik. 1953; 1953(4/5): 209-213. German.
     Google Scholar
  10. Bracewell RN. The maximum of the Planck energy spectrum. Nature (London). 1954; 4429: 563-564.
     Google Scholar
  11. Gurevich MM. On the spectral distribution of radiant energy. Uspekhi Fizicheskikh Nauk. 1955; 56(3): 417-424.
     Google Scholar
  12. Sapozhnikov RA. Spectral distribution of radiant energy. Soviet Physics Uspekhi. 1960; 3(1): 172-174.
     Google Scholar
  13. Chiu WC. On the interpretation of the energy spectrum. American Journal of Physics. 1967; 35(7): 642-648.
     Google Scholar
  14. Soffer BH, Lynch DK. Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision. American Journal of Physics, 1999; 67(11): 946-953.
     Google Scholar
  15. Overduin JM. Eyesight and the Solar Wien peak. American Journal of Physics, 2003; 71(3): 216-219.
     Google Scholar
  16. Heald MA. Where is the “Wien peak”? American Journal of Physics, 2003; 71(12): 1322-1323.
     Google Scholar
  17. Kramm G, Mölders N. Planck´s blackbody radiation law: presentation in different domains and determination of the related dimensional constants. Arxiv: 0901.1863v2. [Accessed on January 29, 2023].
     Google Scholar
  18. Zhang ZM, Wang XJ. Unified Wien´s displacement law in terms of logarithmic frequency or wavelength scale. Journal of Thermophysics and Heat Transfer. 2010; 24(1): 222-224.
     Google Scholar
  19. Stewart SM. Wien peaks and the Lambert W function. Revista Brasileira de Ensimo de Física. 2011; 33(3): 3308.
     Google Scholar
  20. Stewart SM. Spectral peaks and Wien´s displacement law. Journal of Thermophysics ad Heat Transfer. 2012; 26(4): 689-691.
     Google Scholar
  21. Marr JM, Wilkin FP. A better presentation of Planck´s radiation law. Arxiv: 1109.3822v3. [Accessed on January 29, 2023].
     Google Scholar
  22. Deldago-Bonal A. Entropy of radiation: the unseen side of light. Scientific Reports. 2017; 7: 1642.
     Google Scholar
  23. Hagen N. Spectra, images, simple functions, and density functions. 2021 11th Workshop on hyperspectral imaging and signal processing: evolution in remote sensing (WHISPERS), Amsterdam, Netherlands, 2021, pp. 1-5.
     Google Scholar
  24. Kostić L, Mančev I. Lambert W function ad different forms of Wien´s displacement law. Romanian Reports in Physics. 2021; 73: 906.
     Google Scholar
  25. Calculation of blackbody radiance. Arxiv: 2108.03119. [Accessed on January 29, 2023].
     Google Scholar
  26. Gnanarajan S. Application of Lambert W function to Planck spectral radiance frequencies. Journal of Applied Mathematics and Physics, 2021; 9: 2500-2510.
     Google Scholar
  27. Wikipedia. Plancksches Strahlungsgesetz. Retrieved from: https://de.wikipedia.org/wiki/Plancksches_Strahlungsgesetz.
     Google Scholar
  28. Hentschel K. Unsichtbares Licht? Dunkle Wärme? Chemische Strahlen? Eine wissenschaftshistorische und -theoretische Analyse von Argumenten für das Klassifizieren von Strahlungsorten 1650-1925 mit Schwerpunkt auf den Jahren 1770-1900. GNT-Verlag GmbH, 2007. ISBN-10: 3928186841. German.
     Google Scholar
  29. Callender H. The caloric theory of heat and Carnot´s principle. Proc. Phys. Soc. London. 1911; 23: 153-198.
     Google Scholar
  30. Cajori F. On the history of caloric. Isis. 1922; 4(3): 483-492.
     Google Scholar
  31. Brown SC. The caloric theory of heat. American Journal of Physics. 1950; 18(6): 367-373.
     Google Scholar
  32. Kuhn TS. The caloric theory of adiabatic compression. Isis. 1958; 49(2(: 132-140.
     Google Scholar
  33. Kargon R. The decline of the caloric theory of heat: A case study. Centaurus. 1964; 10(1): 35-39.
     Google Scholar
  34. Brush SG. The wave theory of heat: a forgotten stage in the transition from caloric theory to thermodynamics. The British Journal for History of Science. 1970; 5(2): 145-167.
     Google Scholar
  35. Fox R. The caloric theory of gases. Clarendon Press, Oxoford. 1971.
     Google Scholar
  36. Job G. Neudarstellung der Wärmelehre – Die Entropie als Wärme. Akademische Verlagsgesselschaft. Frankfurt, Germany. 1972. German.
     Google Scholar
  37. Morris RJ. Lavoisier and the caloric theory. The British Journal for the History of Science. 1972; 6(1): 1-38.
     Google Scholar
  38. Falk G. Entropy, a resurrection of caloric. A look at the history of thermodynamics. Eur. J. Phys. 1985; 6: 108-115.
     Google Scholar
  39. Mareš JJ, Hubík P, Šesták J, Špička V, Krištofík J, Stávek J. Phenomenological approach to the caloric theory of heat. Thermochimica Acta. 2008; 474: 1-24.
     Google Scholar
  40. Fuchs HU. The Dynamics of Heat – A unified approach to thermodynamics and heat transfer. (2nd ed). Springer, New York, USA. 2010.
     Google Scholar
  41. Herrman F, Pohling M. Which physical quantity deserves the name “quantity of heat”? Entropy. 2021; 23, 1078.
     Google Scholar
  42. Feldhoff A. On the thermal capacity of solids. Entropy. 2022; 24: 479.
     Google Scholar
  43. Stávek J. What is hidden in the Planck distribution function and the Wien´s peaks? I. Three features of the Solar photons. European Journal of Applied Physics. 2023; 5(2): 1-8.
     Google Scholar
  44. Stávek J. What is hidden in the Planck distribution function and the Wien´s peaks? II. Do atoms fuse Solar photons into gravitons? European Journal of Applied Physics. 2023; 5(2): 9-16.
     Google Scholar
  45. Chang SL, Rhee KT. Blackbody radiation functions. International Communications in Heat and Mass Transfer. 1984; 11(5): 451-455.
     Google Scholar
  46. Jain PK. IR, visible, and UV components in the spectral distribution of blackbody radiation. Physics Education, 1996; 31:149-155.
     Google Scholar
  47. Lawson D. A Closer Look at Planck´s Blackbody Equation. Physics Education. 1997; 35(5): 321-326.
     Google Scholar
  48. Lawson DL. The blackbody fraction, infinite series and spreadsheets. International Journal of Engineering Education. 2004; 20(6): 984-900.
     Google Scholar
  49. Wikipedia. Earth´s energy budget. Retrieved from: https://en.wikipedia.org/wiki/Earth%27s_energy_budget.
     Google Scholar
  50. Stávek J. Solar radiant heat reflected on the Termination shock might create excess microwave radiation in the horn antenna (Thermal telescope). European Journal of Applied Physics. 2022; 4(3): 38-43.
     Google Scholar
  51. Carnot S. Réflexions sur la Puissance Motrice du Feu et Sur es Machines Propres à Développer Cette Puissance. Chez Bachelier, Paris, France, 1824. French.
     Google Scholar
  52. Helmholtz HV. Űber die Erhaltung der Kraft. Vortrag vor der Physikalschen Gesselschft, Berlin, Reimer, 1847. Retrieved from: https://edoc.hu-berlin.de/bitstream/handle/18452/1030/h260_helmholtz_1847.pdf?sequence=1&isAllowed=y.
     Google Scholar
  53. Eucken A. Die Theorie der Strahlung und der Quanten. Verhandlungen auf einer von E. Solvay einberufenen Zusammenkunft (30. Oktober bis 3. November 1911), mit einem Anhang über die Entwicklung der Quantentheorie vom Herbst 1911 bis Sommer 1913. Knapp, Halle a.S. (1914). German.
     Google Scholar
  54. Reiche F. Die Quantentheorie. Naturwissenschaften, 1913; 1: 549-552 and 568-571. German.
     Google Scholar
  55. de Broglie M. Les Premiers congrès de physique Solvay et l´orientation de la physique depuis 1911. Cahiers de la collection Sciences d´Aujourd´hui, dirigés par André George, Paris, Albin Michel, (1951). French.
     Google Scholar
  56. Mehra J. The Solvay Conferences on Physics: Aspects of the Development of Physics since 1911. D. Reichel, Dordrecht, Holland, (1975).
     Google Scholar
  57. Kormos-Barkan D. The Witches´Sabbath: The First International Solvay Congress in Physics. Science in Context, 1993; 6: 59-82.
     Google Scholar
  58. Marage P, Wallenborn G. (Eds.). The Solvay Councils and the Birth of Modern Physics. Birkhäuser Verlag; 1999.
     Google Scholar
  59. Galison P. Solvay Redivivus. In: The Quantum Structure of Space and Time, Proceedings of the 23rd Solvay Conference on Physics, Brussels, Belgium, 1-3 December, 2005, Eds. D. Gross, M. Henneaux, and A. Servin, World Scientific, New Jersey, (2007).
     Google Scholar
  60. Straumann N. On the first Solvay Congress in 1911. The European Physical Journal H, 2011; 36: 379-399.
     Google Scholar
  61. Lambert F, Berends F, Eckert M. The early Solvay councils and the advent of the quantum Era. The European Physical Journal Special Topics, 2015; 224: 2011-2021.
     Google Scholar
  62. Lambert FJ. Einstein´s witches´ sabbath in Brussels: The legend and facts. The European Physical Journal Special Topics, 2015; 224: 2023-2040.
     Google Scholar
  63. Foucart S. Au Métropole un sabbath de sorcières”. Le Monde, 2015; 31 July. French.
     Google Scholar
  64. Lambert F, Berends F. Einstein´s Witches´Sabbath and the Early Solvay Councils: The Untold Story. Kindle Edition, EDP Sciences (November 18, 2021).
     Google Scholar
  65. Einstein A. Planck´s theory of radiation and the theory of specific heat. Annalen der Physik, 1907; 22: 180-190.
     Google Scholar
  66. Einstein A. Elementary Observations on Thermal Molecular Motion in Solids-Note Added in Proof. Annalen der Physik, 1911; 35: 679-694.
     Google Scholar
  67. Nernst W, Lindemann FA. Untersuchung über die spezifische Wärme bei tiefen Temperaturen. V. Sitzungsberichte der Berl. Akad. der Wiss.; 1911: 492-501. German.
     Google Scholar
  68. Nernst W, Lindemann FA. Spezifische Wärme und Quantentheorie. Zeitschrift für Elektrochemie, 1911; 18: 817-827. German.
     Google Scholar
  69. Kormos-Barkan D. Walther Nernst and the Transition to Modern Physical Science. Cambridge University Press, Cambridge; 1999.
     Google Scholar
  70. Debye P. Zur Theorie der spezifischen Wärmen. Annalen der Physik. 1912; 39: 789-839. German.
     Google Scholar
  71. Sackur O. Lehrbuch der Thermochemie und Thermodynamics. Berlin, Julius Springer; 1912. German.
     Google Scholar
  72. Griffiths EH, Griffiths E. The Capacity for Heat of Metals at Low Temperatures. Phil. Trans. Royal Soc. Series A, Containing Papers of a Mathematical or Physical Character, 1914; 214: 319-357.
     Google Scholar
  73. Sieveking H. Moderne Probleme der Physik. Vieweg Verlag, Braunschweig; 1914: 142. German.
     Google Scholar
  74. Richardson OW. The Electron Theory of Matter. Cambridge University Press, Cambridge; 1914.
     Google Scholar
  75. Valentiner S. Anwendung der Quantenhypothese in der kinetischen Theorie der festen Körper und der Gase in elementaler Darsttellung. Vieweg Verlag, Brauschweig; 1921. German.
     Google Scholar
  76. Reiche F. Die Quantentheorie. Ihr Ursprung und ihre Entwicklung. Springer Verlag, Berlin; 1921. German.
     Google Scholar
  77. Lindemann F. Guthrie Lecture: Prof. F.A: Lindemann, F.R.S. Nature, 1936: 809.
     Google Scholar
  78. Born M, von Kármán T. Zur Theorie der Spezifischen Wärmen. Physikalische Zeitschrift, 1913; 14: 15-19. German.
     Google Scholar
  79. Nath NN. The dynamical theory of the diamond lattice. Proceedings of the Indian Academy of Sciences, Section A, 1935: 143-152.
     Google Scholar
  80. Klein MJ. Einstein, Specific Heats, and the Early Quantum Theory. Science, New Series, 1965; 148: 173-180.
     Google Scholar
  81. Pais A. Einstein and the quantum theory. Reviews of Modern Physics, 1979; 51: 863-914.
     Google Scholar
  82. Hulin M. En attendant Debye. Eur. J. Phys., 1980; 1: 222-224.
     Google Scholar
  83. Mehra J, Rechenberg H. The Quantum Theory of Planck, Einstein, Bohr, and Sommerfeld: Its Foundation and the Rise of Its Difficulties 1900-1925. In: The historical Development of Quantum Theory, vol. 1, part 1, Springer Verlag, New York; 1982.
     Google Scholar
  84. Kox AJ. Einstein, Specific Heats, and Residual Rays: The History of a Retracted Paper. In: No Truth Except in the Details, Eds.: A.J. Kox and D.M. Siegel, Kluwer Academic Publishers, (1995).
     Google Scholar
  85. Pérez E. Einstein i la calor expecífica dels sòlids: arguments per a una teoria quàntica. Revista de Física, 2007; 4: 34-48.
     Google Scholar
  86. Irons FE. New method for reducing the general formula for lattice specific heat to the Einstein and Nernst-Lindemann approximations. Canadian Journal of Physics, 2011; 81: 1015-1036.
     Google Scholar
  87. Tosto S. Reappraising 1907 Einstein´s Model of Specific Heat. Open Journal of Physical Chemistry, 2016; 6:109-128.
     Google Scholar
  88. Stávek J. A new interpretation of contributions presented at the Solvay conference 1911. Can we falsify the “geocentric” foundations of quantum mechanics in the Solar System? European Journal of Applied Physics. 2021; 3(6): 61-65.
     Google Scholar
  89. Fitzgerel RK, Verhoek FH. The law of Dulong and Petit. Journal of Chemical Education. 1960; 37(10): 545-549.
     Google Scholar
  90. Fox R. The background to the Discovery of Dulong and Petit´s law. The British Journal for the History of Science. 1968; 4(1): 1-22.
     Google Scholar
  91. Piazza R. The strange case of Dr. Petit and Mr. Dulong. Arxiv: 1807.02270v1. Accessed on January 31, 2023.
     Google Scholar
  92. Oudet X. The black body and the Dulong and Petit law. Annales de la Foundation Louis de Broglie. 2005; 30(1): 97-108.
     Google Scholar
  93. Laing Ma, Laing Mi. Dulong and Petit´s law: we should not ignore its importance. Journal of Chemical Education. 2006; 83(10): 1499-1504.
     Google Scholar
  94. Stávek J. European Journal of Applied Physics. Submitted.
     Google Scholar
  95. Clausius R. Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. Ann.Phys.Chem. 1865; 201, 390. German.
     Google Scholar
  96. Rankine WJM. On the centrifugal theory of elasticity, and its connection with the theory of heat. Earth and Enviromental Science Transactions of the Royal Society of Edinburgh. 1853; 20(3): 425-440.
     Google Scholar
  97. Fuchs HU, D´Anna M, Corni F. Entropy and the experience of heat. Entropy. 2022; 24, 646.
     Google Scholar
  98. Chen M. What is heat? SCIREA Journal of Physics. 2022; 7(6): 244-258.
     Google Scholar
  99. Petit AT, Dulong PL. Remarks on some important points of the theory of heat. Annals of Philosophy. 1819; 14: 189-198.
     Google Scholar


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