Abstract
The general concept of temperature is thermodynamically defined in equilibrium somehow predictable even for non-equilibrium; however, it presents some still controversial aspects, as has been shown in a number of studies and reviews that have been published so far. Equilibrium concepts are often extrapolated to apply in micro-localized equilibrium and then appended to non-equilibrium in its entirety, which helps to define out-of-equilibrium temperature on both the macroscopic and microscopic bases. Unfortunately, these theoretical analyses do not provide any guidance on how to assess and understand temperature in practical measurements, such as for conventional thermal analysis. Insufficient use of alternative thermodynamic attitudes is evident especially in the field of thermophysical studies, which do not use static measurements, because they usually involve heating from an external source, i. e., the effect of thermal dynamics on the laboratory sample. This paper presents the applied nonequilibrium thermodynamic concept, historically known as thermotics. This approach takes into account the existence of gradients and heat fluxes, which it assesses from the point of view of the average user, and considers additional influences, going beyond the description of thermodynamics in traditional textbooks. The goal is to extend their validity, even to the state of constant first-time derivatives. At the same time, it points to changes in the temperature due to thermal inertia, which has long been ignored, suggesting that the heat spreads immediately. Moreover, special techniques enabling measurements during its extreme changes probably then require an alternative concept for temperature (tempericity). This opinion paper may provide stimuli for further discussion with regard to the practice of measurements done in the customary nonisothermal mode.
Funding source: Grantová Agentura České Republiky
Award Identifier / Grant number: 20-00653S
Funding statement: This research has been supported by the Czech Science Foundation, under project No. 20-00653S.
Acknowledgment
The authors appreciate Michal Pavelka for his contribution to the worthy organization of the JETC conference in Prague 2021 and the support of the ideas included in this paper.
References
[1] L. Balamuth, H. C. Wolfe and M. W. Zemansky, The temperature concept from the macroscopic point of view, Am. J. Phys. 9 (1941), 199–203.10.1119/1.1991676Search in Google Scholar
[2] J. Casas-Vázquez and D. Jou, Temperature in non-equilibrium states: a review of open problems and current proposals, Rep. Prog. Phys. 66 (2003), 1937–1957.10.1088/0034-4885/66/11/R03Search in Google Scholar
[3] A. Puglisi, A. Sarracino and A. Vulpiani, Temperature in and out of equilibrium: a review of concepts, tools and attempts, Phys. Rep. 709 (2017), 1–110.10.1016/j.physrep.2017.09.001Search in Google Scholar
[4] H. Hoshino and S. Nakamura, Proper effective temperature of nonequilibrium steady state. Prog. Theor. Exp. Phys. 2020 (2020) 093B09. DOI: 10.1093/ptep/ptaa110.Search in Google Scholar
[5] U. Lucia and G. Grisolia, Nonequilibrium temperature: an approach from irreversibility, Materials 14 (2004), 2021.10.3390/ma14082004Search in Google Scholar PubMed PubMed Central
[6] M. Holeček, J. J. Mareš and J. Šesták, What is the physical and operational meaning of temperature and its self-measurability during unsteady thermal processes within thermodynamic concepts, in: J. Šesták, P. Hubík, J. J. Mareš (eds.), Thermal Physics and Thermal Analysis, Springer, Berlin, 2017, pp. 45–47.10.1007/978-3-319-45899-1_3Search in Google Scholar
[7] M. Tribus, Thermostatics and Thermodynamics: An Introduction to Energy, Information and States of Matter, Nostrand, New York, 1961.Search in Google Scholar
[8] M. Wayne and A. Saslow, History of thermodynamics: the missing manual, Entropy 22 (2020), 77.10.3390/e22010077Search in Google Scholar PubMed PubMed Central
[9] J. Šesták, J. J. Mareš, P. Hubík and I. Proks, Contribution by Lazare and Sadi Carnot to the caloric theory of heat and its inspirative role in alternative thermodynamics, J. Therm. Anal. Calorim. 97 (2009), 679–683.10.1007/s10973-008-9710-ySearch in Google Scholar
[10] C. Eckart, Thermodynamics of irreversible processes, Phys. Rev. 58 (1940), 267.10.1103/PhysRev.58.267Search in Google Scholar
[11] I. Prigogine, Introduction to the Thermodynamics of Irreversible Processes, Wiley/Interscience, New York, 1967.Search in Google Scholar
[12] H. Hollinger and M. Zeusen, The Nature of Irreversibility, Reidel, Dordrecht, 1985.10.1007/978-94-009-5430-4Search in Google Scholar
[13] I. Müller and T. Ruggeri, Extended Rational Thermodynamics, Springer, New York, 1998.10.1007/978-1-4612-2210-1Search in Google Scholar
[14] H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley, New York, 2005.10.1002/0471727903Search in Google Scholar
[15] W. Muschik, Why so many “schools” of thermodynamics?, Forsch. Ingenieurwes. 71 (2007), 149–161.10.1007/s10010-007-0053-9Search in Google Scholar
[16] G. Lebon and D. Jou, Early history of extended irreversible thermodynamics: An exploration beyond local equilibrium and classical transport theory, Eur. Phys. J. H 40 (2015), 205–240.10.1140/epjh/e2014-50033-0Search in Google Scholar
[17] G. O. Piloyan, Introduction to the Theory of Thermal Analysis, Izd. Nauka, Moskva, 1964 (in Russian).Search in Google Scholar
[18] P. D. Garn, Thermal Analysis of Investigation, Academic Press, New York, 1965.Search in Google Scholar
[19] J. Šesták, Thermophysical Properties of Solids: Theoretical Thermal Analysis, Elsevier, Amsterdam, 1984; and Russian translation by Mir, Moscow, 1988.Search in Google Scholar
[20] R. Černý and P. Rovnaníková, Transport Processes in Concrete, SponPress, London, 2002.10.1201/9781482289107Search in Google Scholar
[21] M. V. Zemansky and R. Dittman, Heat and Thermodynamics, McGraw-Hill, New York, 2006.Search in Google Scholar
[22] Y. A. Cengel, Introduction to Thermodynamics and Heat Transfer, McGraw-Hill, New York, 2009.Search in Google Scholar
[23] H. U. Fuchs, Dynamics of Heat: A Unified Approach to Thermodynamics and Heat Transfer, Springer, New York, 2010.10.1007/978-1-4419-7604-8Search in Google Scholar
[24] B. Golding, Two chapters on thermotics, in: Elements of Natural Philosophy: The Study of the Physical Sciences, John Churchill, London, 1839.Search in Google Scholar
[25] J. Brønsted, Principles and Problems in Energetics, Interscience, New York, 1955.Search in Google Scholar
[26] J. Šesták, Thermodynamic basis for the theoretical description and correct interpretation of thermoanalytical experiments, Thermochim. Acta 28 (1979), 197–227.10.1016/0040-6031(79)85126-6Search in Google Scholar
[27] R. J. Tykodi, Thermodynamics of Steady State, MacMillan, New York, 1967.Search in Google Scholar
[28] R. J. Tykodi, Correspondence: thermodynamics – thermotics as the name of the game, Ind. Eng. Chem. 60 (1968), 22.10.1021/ie50707a006Search in Google Scholar
[29] P. Holba, The Šesták’s proposal of term “tempericity” for non-equilibrium temperature and modified Tykodi’s thermal science classification with regards to the methods of thermal analysis, J. Therm. Anal. Calorim. 127 (2017), 2553–2559.10.1007/s10973-016-5659-4Search in Google Scholar
[30] M. Holeček, Self-measurability in rapid thermal processes, J. Therm. Anal. Calorim. 120 (2015), 217–221.10.1007/s10973-015-4541-0Search in Google Scholar
[31] J. Šesták, Measuring “hotness”, should the sensor’s readings for rapid temperature changes be named “tempericity”?, J. Therm. Anal. Calorim. 125 (2016), 991–999.10.1007/s10973-016-5455-1Search in Google Scholar
[32] J. Šesták, Do we really know what temperature is: from Newton’s cooling law to an improved understanding of thermal analysis, J. Therm. Anal. Calorim. 142 (2020), 913–926.10.1007/s10973-019-09149-wSearch in Google Scholar
[33] P. Holba and J. Šesták, Kinetics with regards to the equilibrium of processes studied at increasing temperatures, Z. Phys. Chem. N. F. 80 (1972), 1–20.10.1524/zpch.1972.80.1_2.001Search in Google Scholar
[34] J. A. Lerchner, G. Wolf and J. Wolf, Recent developments in integrated circuit calorimetry, J. Therm. Anal. Calorim. 57 (1999), 241.10.1023/A:1010152517237Search in Google Scholar
[35] S. A. Adamovsky, A. A. Minakov and C. Schick, Scanning microcalorimetry at high cooling rates, Thermochim. Acta 403 (2003), 55–63.10.1016/S0040-6031(03)00182-5Search in Google Scholar
[36] A. A. Minakov and C. Schick, Dynamics of the temperature distribution in ultra-fast thin-film calorimeter sensors, Thermochim. Acta 603 (2015), 205–217.10.1016/j.tca.2014.05.030Search in Google Scholar
[37] J. Šesták, Kinetic phase diagrams as consequence of radical changing temperature or particle size, J. Therm. Anal. Calorim. 120 (2015), 129–137.10.1007/s10973-014-4352-8Search in Google Scholar
[38] M. I. Davidzon, Newton’s cooling law and its interpretation, Int. J. Heat Mass Transf. 55 (2012), 5397–5402.10.1016/j.ijheatmasstransfer.2012.03.035Search in Google Scholar
[39] M. J. Vold, Differential thermal analysis, Anal. Chem. 21 (1949), 683–688.10.1021/ac60030a011Search in Google Scholar
[40] P. Holba and J. Šesták, Heat inertia and its role in thermal analysis, J. Therm. Anal. Calorim. 121 (2015), 303–307.10.1007/s10973-015-4486-3Search in Google Scholar
[41] J. Šesták, Are nonisothermal kinetics fearing historical Newton’s cooling law, or are just afraid of inbuilt complications due to undesirable thermal inertia?, J. Therm. Anal. Calorim. 134 (2018), 1385–1393.10.1007/s10973-018-7705-xSearch in Google Scholar
[42] A. Tian, Recherches sur le Thermostats; Contribution a l’étude du reglage – thermostats a engeintes multiples, J. Chim. Phys. (1923) 132–166.10.1051/jcp/1922200132Search in Google Scholar
[43] E. Calvet and H. Prat, Recent Progress in Microcalorimetry, Pergamon Press, Oxford, 1963.Search in Google Scholar
[44] J. Šesták, The evaluation of non-isothermal thermoanalytical kinetics is simplified without the description of heat transfers, such as thermal inertia, which is not negligible, Int. J. Chem. Kinet. 53 (2021), 1050–1057.10.1002/kin.21495Search in Google Scholar
[45] J. Šesták, Dynamic character of thermal analysis where thermal inertia is a real and not negligible effect influencing the evaluation of nonisothermal kinetics: a review, Thermo 2 (2021), 220.10.3390/thermo1020015Search in Google Scholar
[46] D. Klimm, Thermal Analysis and Thermodynamics in Materials Science, De Gruyter, Berlin, 2022. ISBN: 9783110743784.10.1515/9783110743784Search in Google Scholar
[47] J. Šesták, Thermal Analysis and Thermodynamic Properties of Solids, Elsevier, Amsterdam, 2021. ISBN: 9780323855372.Search in Google Scholar
[48] E. D. Eastman, Thermodynamics of non-isothermal systems, J. Am. Chem. Soc. 48 (1926), 1482–1493.10.1021/ja01417a004Search in Google Scholar
[49] J. C. M. Li, Thermodynamics for non-isothermal systems: The classical formulation, J. Chem. Phys. 29 (1958), 747.10.1063/1.1744586Search in Google Scholar
[50] J. Šesták, Some thermodynamic aspects of non-equilibrium glassy state, Thermochim. Acta 95 (1985), 459–471.10.1016/0040-6031(85)85312-0Search in Google Scholar
[51] J. M. Rubi and A. Perez-Madrid, Inertial effects in non-equilibrium thermodynamics, Physica A 264 (1999), 492–502.10.1016/S0378-4371(98)00476-2Search in Google Scholar
[52] Y. Demirel and S. I. Sandler, Non-equilibrium thermodynamics in engineering and science, J. Phys. Chem. B 108 (2004), 31–43.10.1021/jp030405gSearch in Google Scholar
[53] M. B. Saihanov, Simulation of irreversible processes in non-isothermal systems, High Temp. 44 (2006), 871–878.10.1007/s10740-006-0105-0Search in Google Scholar
[54] M. Schweizer and L. M. C. Sagis, Nonequilibrium thermodynamics of nucleation, J. Chem. Phys. 141 (2014), 224102.10.1063/1.4902885Search in Google Scholar PubMed
[55] S. Gladkov, J. Kochmann, S. Reese, M. Hütter and B. Svendsen, Thermodynamic model formulations for inhomogeneous solids with application to non-isothermal phase field modelling, J. Non-Equilib. Thermodyn. 41 (2016), 131–139.10.1515/jnet-2015-0062Search in Google Scholar
[56] V. Kočí, J. Kočí, H. J. Maděra and R. Černý, Assessment of fast heat evolving processes using inverse analysis of calorimetric data, Int. J. Heat Mass Transf. 115 (2017), 831–838.10.1016/j.ijheatmasstransfer.2017.07.118Search in Google Scholar
[57] Q. X. Le and V. Dao, Effects of temperature and temperature gradient at elevated temperatures, Adv. Struct. Eng. 21 (2018), 1223–1233.10.1177/1369433217746347Search in Google Scholar
[58] K. Shirai, A thermodynamic description of non-equilibrium glassy state and the glass transition, J. Phys. Commun. 4 (2020), 085015.10.1088/2399-6528/abae16Search in Google Scholar
[59] S. Y. Misyura, Different modes of heat transfer and crystallization in a drop solution: The influence of key factors, Int. J. Therm. Sci. 159 (2021), 106602.10.1016/j.ijthermalsci.2020.106602Search in Google Scholar
[60] V. N. Sapunov, E. A. Saveljev, M. S. Voronov, M. Valtiner and W. Linert, The basic theorem of temperature-dependent processes, Thermo 1 (2021), 1–17.10.3390/thermo1010004Search in Google Scholar
[61] V. Chaurasiva, K. N. Rai and J. Singh, Heat transfer analysis for the solidification of a binary eutectic system under imposed movement of the material, J. Therm. Anal. Calorim. 147 (2022), 3229–3246.10.1007/s10973-021-10614-8Search in Google Scholar
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