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তাপীয় সাম্যাবস্থা: সংশোধিত সংস্করণের মধ্যে পার্থক্য

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৬,৪৩৯টি সম্পাদনা
Jdebabrata (আলোচনা | অবদান)
৬,৪৩৯টি সম্পাদনা
৩৭ নং লাইন:
 
One may consider a system contained in a very tall adiabatically isolating vessel with rigid walls initially containing a thermally heterogeneous distribution of material, left for a long time under the influence of a steady gravitational field, along its tall dimension, due to an outside body such as the earth. It will settle to a state of uniform temperature throughout, though not of uniform pressure or density, and perhaps containing several phases. It is then in internal thermal equilibrium and even in thermodynamic equilibrium. This means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40" /> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{Cite journal | doi=10.1175/1520-0469(2004)061<0931:OMEP>2.0.CO;2| bibcode=2004JAtS...61..931V| issn=1520-0469| year=2004| volume=61| pages=931–936| title=On Maximum Entropy Profiles| last1=Verkley| first1=W. T. M.| last2=Gerkema| first2=T.| journal=Journal of the Atmospheric Sciences| issue=8| doi-access=free}}</ref><ref>Akmaev, R.A. (2008). On the energetics of maximum-entropy temperature profiles, ''Q. J. R. Meteorol. Soc.'', '''134''':187–197.</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>Coombes, C.A., Laue, H. (1985). A paradox concerning the temperature distribution of a gas in a gravitational field, ''Am. J. Phys.'', '''53''': 272–273.</ref><ref>Román, F.L., White, J.A., Velasco, S. (1995). Microcanonical single-particle distributions for an ideal gas in a gravitational field, ''Eur. J. Phys.'', '''16''': 83–90.</ref><ref>Velasco, S., Román, F.L., White, J.A. (1996). On a paradox concerning the temperature distribution of an ideal gas in a gravitational field, ''Eur. J. Phys.'', '''17''': 43–44.</ref>
 
==Distinctions between thermal and thermodynamic equilibria==
 
There is an important distinction between thermal and [[thermodynamic equilibrium]]. According to Münster (1970), in states of thermodynamic equilibrium, the state variables of a system do not change at a measurable rate. Moreover, "The proviso 'at a measurable rate' implies that we can consider an equilibrium only with respect to specified processes and defined experimental conditions." Also, a state of thermodynamic equilibrium can be described by fewer macroscopic variables than any other state of a given body of matter. A single isolated body can start in a state which is not one of thermodynamic equilibrium, and can change till thermodynamic equilibrium is reached. Thermal equilibrium is a relation between two bodies or closed systems, in which transfers are allowed only of energy and take place through a partition permeable to heat, and in which the transfers have proceeded till the states of the bodies cease to change.<ref>Münster, A. (1970), pp. 6, 22, 52.</ref>
 
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by C.J. Adkins. He allows that two systems might be allowed to exchange heat but be constrained from exchanging work; they will naturally exchange heat till they have equal temperatures, and reach thermal equilibrium, but in general will not be in thermodynamic equilibrium. They can reach thermodynamic equilibrium when they are allowed also to exchange work.<ref>Adkins, C.J. (1968/1983), pp. 6–7.</ref>
 
Another explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which several irreversible processes are occurring. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."<ref>Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, {{ISBN|1-4020-0788-4}}, page 13.</ref>
 
==উদ্ধৃতি==
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