A New Interpretation of the Newton´s Cooling Law: Two Features of Thermons: Their Elastic Volume and Their Angular Momentum



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Submitted Apr 25, 2023
Published Jun 1, 2023
10.24018/ejphysics.2023.5.3.262

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The Newton´s cooling law still attracts the attention of scholars in order to describe hidden features of heat particles (thermons) and the mechanism of the radiating heat into the surroundings with a lower temperature. The characteristic cooling constant of this process 1/τπ [min-1] was defined as the experimental parameter describing the contributions of the thermon elastic volume and thermon angular momentum. This experimental parameter τπwas found as the time needed to achieve the temperature Tπ = Tenv +(T0-Tenv)/π during the cooling of the studied object with the starting temperature T0 and the surrounding with temperature Tenv. The studied system was water in spherical flasks with the volumes 2000, 1000, 500, 250, and 100 mL and the starting temperatures 90° C, 80°C, and 70° C. The temperature of the surrounding was 24° C (laboratory temperature) and (4° ± 2°) C (outdoor temperature on March 5 2023 near Prague). There was one critical experimental parameter: where to place the thermometer in the spherical flask: 1. inside to the bottom wall, 2. in the center of spherical flask, 3. at the upper level of the water volume, 4. outside to the bottom wall. For all experimental runs we have found that the temperature Tπ measured at the inside bottom wall of the spherical flasks might be interpreted as the “true” Newtonian temperature while the characteristic cooling constant τπ is very close to the value of the slope in the semi-log graph of those cooling systems. This model was used to interpret the historical experimental data of Newton (1701) and the modern experimental data of Grigull (1984). This model opens a new view on the Carnot engine where the elastic volume of thermons can achieve the efficiency η1 = (THOT – Tπ)/(THOT – TCOLD) = 1-1/π ≈ 0.682. Moreover, the “waste heat” after the Carnot engine can be used in the Seebeck generator to convert the angular momentum of thermons into the electricity (thermoelectric generator) with the efficiency η2 = (Tπ –TCOLD)/(THOT – TCOLD) = 1/π ≈ 0.318. The combined Carnot (1824) – Seebeck (1825) engine can explore all available heat of the of thermons for the temperature difference THOT – TCOLD.
Keywords: Carnot Heat Engine Measure of the Quantity of Heat S Newton´s Cooling Law Seebeck Generator Thermon Angular Momentum Thermon Elastic Volume Thermon Transfer of Heat

References

  1. Anonymous. Scala graduum caloris. Philosophical Transactions of the Royal Society of London. 1701; 22, 824-829. Latin.
     Google Scholar
  2. Richmann GW. Inquisito in legem, secundum quam calor fluidi in vase contenti, certo temporis intervallo, in temperie aëris constanter eadem decresit vel crescit. Novi Commentari Academiae Scientiarum Imperialis Petropolitanane. 1747; 174-197. Latin.
     Google Scholar
  3. Erxleben ICP. Legem vulgarem, secundum quam calor corporum certo temporis intervallo crescere dicitur, ad examen revocat. Novi Commentarii Societatis Regiae Scientiarum Gottingensis. 1777, Gottingae, VIII, 74-95. Latin.
     Google Scholar
  4. Thomson B. (Rumford). An enquiry concerning the nature of heat and the mode of its communication. Philosophical Transactions of the Royal Society. 1804; 94, 77-182.
     Google Scholar
  5. Biot M. Sur la loi de Newton relative à la communication de la chaleur. Bulletin de la Société Philomatique. 1816; 21-24. French.
     Google Scholar
  6. Dulong P, Petit A. Recherches sur la Mesure des Températures et sur les Lois de la communication de la chaleur. Annales de Chimie et de Physique. 1817; VII. 113-154, 225-264, 337-367. French.
     Google Scholar
  7. Stefan J. Űber die Beziehung zwischen der Wärmestrahlung und der Temperatur. Sitzungsberichte der mathematischen-naturwissenschaftlichen Classe der kaiserlichen Akademie der Wissenschaften. 1879; 79, 391-428. German.
     Google Scholar
  8. Ruffner JA. Reinterpretation of the genesis on Newton´s “Law of Cooling”. Archive for History of Exact Sciences. 1963; 2(2): 138-152.
     Google Scholar
  9. Molnar GW. Newton´s thermometer: a model for testing Newton´s law of cooling. Physiologist. 1969; 12(1): 9-19.
     Google Scholar
  10. Grigull U. Newton´s temperature scale and the law of cooling. Wärme-Stoffübertragung. 1984; 18, 195-199.
     Google Scholar
  11. O‘Sullivan CT. Newton law of cooling – a critical assesment. American Journal of Physics. 1990; 58(10): 956-960.
     Google Scholar
  12. Cheng KC, Fujii T. Isaac Newton and heat transfer. Heat Transfer Engineering. 1998; 19(4): 9-21.
     Google Scholar
  13. Winterton RHS. Newton´s law of cooling. Contemporary Physics. 1999; 40(3): 205-212.
     Google Scholar
  14. Winterton RHS. Early study of heat transfer: Newton and Fourier. Heat Transfer Engineering. 2001; 22, 3-11.
     Google Scholar
  15. Wisniak J. Heat radiation – from Newton to Stefan. Indian Journal of Chemical Technology. 2002; 9, 545-555.
     Google Scholar
  16. Simms DL. Newton´s contribution to the science of heat. Annals of Science. 2004; 61(1): 33-77.
     Google Scholar
  17. Cheng KC. Some observations on the origins of Newton´s law of cooling and its influences on thermofluid science. Applied Mechanics Reviews. 2009; 62(6): 060803.
     Google Scholar
  18. Barragán D. Entropy production and Newton´s cooling law. Revista Ingenieria e Investigación. 2009; 29(2): 88-93. Spanish.
     Google Scholar
  19. Vollmer M. Newton´s law of cooling revisited. European Journal of Physics. 2009; 30(5): 1063-1084.
     Google Scholar
  20. Bensson U. The history of the cooling law: when search for simplicity can be an obstacle. Science & Education. 2010; 21(8): 1-26.
     Google Scholar
  21. Panković V, Kapor DV. A modification of the Newton´s cooling law and Mpemba effect. Arxiv. 1005. 1013v1. Accessed on April 25, 2023.
     Google Scholar
  22. Davidzon MI. Newton´s law of cooling and its interpretation. International Journal of Heat and Mass Transfer. 2012; 55: 5397-5402.
     Google Scholar
  23. Šesták J. Are nonisothermal kinetics fearing historical Newton´s cooling law, or are just afraid to inbuilt complications due to undesirable thermal inertia? Journal of Thermal Analysis and Calorimetry. 2018; 134, 1385-1393.
     Google Scholar
  24. Šesták J. Do we really know what temperature is: from Newton´s cooling law to an improved understanding of thermal analysis. Journal of Thermal Analysis and Calorimetry. 2020; 142 (217-21): 1-14.
     Google Scholar
  25. Maruyama S, Moriya S. Newton´s law of cooling: follow up and exploration. International Journal of Heat and Mass Transfer. 2021; 164, 120544.
     Google Scholar
  26. Sarafian H. Alternative cooling model vs Newton´s cooling. American Journal of Computational Mathematics. 2021; 11: 64-69.
     Google Scholar
  27. Zhao B. Integrity of Newton´s cooling law based on thermal convection theory of heat transfer and entropy transfer. Scientific Reports. 2022; 12: 16292.
     Google Scholar
  28. Perea Martins JEM. A data acquisition system for water heating and cooling experiments. Physics Education. 2017; 52: 015019.
     Google Scholar
  29. Rodríguez-Acevedo F, Fiore-Álvarez S, Zúñiga.Campos M, Miranda BC, Mata-Segreda JF. Newton´s cooling rate constant of liquids for the relative assessment for heat transport. International Journal for Renewable Energy & Biofuels. 2018; Article ID 996542.
     Google Scholar
  30. Perea Martins JEM. An experimental analysis of the cooling constant computation. Physics Education. 2022; 57: 025001.
     Google Scholar
  31. Callender H. The caloric theory of heat and Carnot´s principle. Proc. Phys. Soc. London. 1911; 23: 153-198.
     Google Scholar
  32. Larmor J. On the nature of heat as directly deductible from the postulate of Carnot. Proc. Roy. Soc. A. 1918; 94: 326-339.
     Google Scholar
  33. Lunn AC. The measurement of heat and the scope of Carnot´s principle. Physical Review. 1919; 14(1): 1-19.
     Google Scholar
  34. Cajori F. On the history of caloric. Isis. 1922; 4(3): 483-492.
     Google Scholar
  35. Brown SC. The caloric theory of heat. American Journal of Physics. 1950; 18(6): 367-373.
     Google Scholar
  36. Kuhn TS. The caloric theory of adiabatic compression. Isis. 1958; 49(2(: 132-140.
     Google Scholar
  37. Kargon R. The decline of the caloric theory of heat: A case study. Centaurus. 1964; 10(1): 35-39.
     Google Scholar
  38. 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
  39. Fox R. The caloric theory of gases. Clarendon Press, Oxoford. 1971.
     Google Scholar
  40. Job G. Neudarstellung der Wärmelehre – Die Entropie als Wärme. Akademische Verlagsgesselschaft. Frankfurt, Germany. 1972. German.
     Google Scholar
  41. Morris RJ. Lavoisier and the caloric theory. The British Journal for the History of Science. 1972; 6(1): 1-38.
     Google Scholar
  42. Falk G. Entropy, a resurrection of caloric. A look at the history of thermodynamics. Eur. J. Phys. 1985; 6: 108-115.
     Google Scholar
  43. Chang HS. Preservative realism and its discontents: revisiting caloric. Philosophy of Science. 2003; 70(5): 902-912.
     Google Scholar
  44. 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
  45. Šesták J, Mareš JJ, Hubík P, Proks I. Contribution by Lazare and Sadi Carnot to the caloric theory of heat and its inspirative role in thermodynamics. Journal of Thermal Analysis and Calorimetry. 2009; 97: 679-683.
     Google Scholar
  46. Fuchs HU. The Dynamics of Heat – A unified approach to thermodynamics and heat transfer. 2nd edition, Springer, New York, USA. 2010.
     Google Scholar
  47. Roller D. CASE 3. The early development of the concepts of temperature and heat. The rise and decline of the caloric theory. Vol. I. Harvard Case Histories in Experimental Science. Harvard University Press, 2013, pp. 117-214.
     Google Scholar
  48. Herrman F, Pohling M. Which physical quantity deserves the name „quantity of heat?” Entropy. 2021; 23, 1078.
     Google Scholar
  49. Feldhoff A. On the thermal capacity of solids. Entropy. 2022; 24: 479.
     Google Scholar
  50. Daub EE. Entropy and dissipation. Historical Studies in the Physical and Biological Sciences. 1970; 2: 321-354.
     Google Scholar
  51. Kragh H, Weininger J. Sooner silence than confusion: the tortuous entry of entropy into chemistry. Historical Studies in the Physical and Biological Sciences. 1996; 27(1): 91-130.
     Google Scholar
  52. Brissaud JB. The meanings of entropy. Entropy. 2005; 7: 68-96.
     Google Scholar
  53. Čápek V, Sheelan DP. Challenges to the second law of thermodynamics – theory and experiment. Springer, Dordrecht, 2005.
     Google Scholar
  54. Leff HS. Entropy, its language, and interpretation. Foundations of Physics. 2007; 37: 1744-1766.
     Google Scholar
  55. Saslow WM. A history of thermodynamics: the missing manual. Entropy. 2020; 22/77.
     Google Scholar
  56. Wu G, Wu Y. A new perspective of how to understand entropy in thermodynamics. Phys. Educ. 2020; 55: 015005.
     Google Scholar
  57. Mitrovic J. Irreversible thermodynamics of James Watt. Advances in Historical Studies. 2022; 11: 119-128.
     Google Scholar
  58. Fuchs HU, D´Anna M, Corni F. Entropy and the experience of heat. Entropy. 2022; 24, 646.
     Google Scholar
  59. Chen M. What is heat? SCIREA Journal of Physics. 2022; 7(6): 244-258.
     Google Scholar
  60. Stávek J. What is hidden in the Planck distribution function and the Wien´s peaks? III. Fission of Solar photons into thermons (“dark heat”). European Journal of Applied Physics.2023; 5(2): 17-25.
     Google Scholar
  61. Stávek J. The mechanical equivalent of heat interpreted as the angular momentum of thermons. European Journal of Applied Physics. 2023; 5(2): 35-39.
     Google Scholar
  62. Comenius IA. Disquisitiones de caloris et frigoris natura cujus cognition vera in reseranda multa naturae arcana clavis erit. (The nature of heat and cold whose true knowledge will be a key to open many secrets of Nature). Editio Amsterodamenius, 1659. In Opera Omnia [12] Jan Amos Komenský, Academia Prague, 1978.
     Google Scholar
  63. Mackenzie RC, Proks I. Comenius and Black: progenitors of thermal analysis. Thermochimica Acta. 1985; 92: 3-14.
     Google Scholar
  64. Šesták J, Mareš JJ. From caloric to stathmograph and polarography. Journal of Thermal Analysis and Calorimetry. 2007; 88: 763-768.
     Google Scholar
  65. Lomonosow M. Meditationes de caloris et frigoris causa Novi Commentari Academiae Scientiarum Imperialis Petropolitanane. 1747; 206-228. Latin.
     Google Scholar
  66. Shiltsev V. Michail Vasil´evich Lomonosow. Arxiv: 1801.00909. https://arxiv.org/ftp/arxiv/papers/1801/1801.00909.pdf.
     Google Scholar
  67. Rankine WJM. On the cetrifugal theory of elasticity, as applied to gases and vapours. Philosophical Magazine. 1851; 2(14): 509-542.
     Google Scholar
  68. 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
  69. Hutchinson K. Der Ursprung der Entropiefunktion bei Rankine und Clausius. Annals of Science. 1973; 30, 341-364. German.
     Google Scholar
  70. Hutchinson K. WJM Rankine and the rise of thermodynamics. The British Journal for the History of Science. 1981; 14(1): 1-26.
     Google Scholar
  71. Wikipedia. Richmann’s law. Retrieved from: https://en.wikipedia.org/wiki/Richmann%27s_law.
     Google Scholar
  72. Carnot S. Reflexions sur la puissance motrice du feu et sur les machines propres à developper cette puissance. Paris, Bachelier; 1824.
     Google Scholar
  73. Wikipedia. Carnot heat engine. Retrieved from: https://en.wikipedia.org/wiki/Carnot_heat_engine.
     Google Scholar
  74. Seebeck TJ. Magnetische Polarisation der Metalle und Erze durch Temperatur-Differenz. Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin. 1825; 265-373.
     Google Scholar
  75. Wikipedia. Thermoelectric generator. Retrieved from: https://en.wikipedia.org/wiki/Thermoelectric_generator.
     Google Scholar


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