Two varieties of thermal equilibrium
Relation of thermal equilibrium between two thermally connected bodies
The relation of thermal equilibrium is an instance of equilibrium between two bodies, which means that it refers to transfer through a selectively permeable partition of matter or work; it is called a diathermal connection. According to Lieb and Yngvason, the essential meaning of the relation of thermal equilibrium includes that it is reflexive and symmetric. It is not included in the essential meaning whether it is or is not transitive. After discussing the semantics of the definition, they postulate a substantial physical axiom, that they call the "zeroth law of thermodynamics", that thermal equilibrium is a transitive relation. They comment that the equivalence classes of systems so established are called isotherms.Internal thermal equilibrium of an isolated body
Thermal equilibrium of a body in itself refers to the body when it is isolated. The background is that no heat enters or leaves it, and that it is allowed unlimited time to settle under its own intrinsic characteristics. When it is completely settled, so that macroscopic change is no longer detectable, it is in its own thermal equilibrium. It is not implied that it is necessarily in other kinds of internal equilibrium. For example, it is possible that a body might reach internal thermal equilibrium but not be in internal chemical equilibrium; glass is an example. One may imagine an isolated system, initially not in its own state of internal thermal equilibrium. It could be subjected to a fictive thermodynamic operation of partition into two subsystems separated by nothing, no wall. One could then consider the possibility of transfers of energy as heat between the two subsystems. A long time after the fictive partition operation, the two subsystems will reach a practically stationary state, and so be in the relation of thermal equilibrium with each other. Such an adventure could be conducted in indefinitely many ways, with different fictive partitions. All of them will result in subsystems that could be shown to be in thermal equilibrium with each other, testing subsystems from different partitions. For this reason, an isolated system, initially not its own state of internal thermal equilibrium, but left for a long time, practically always will reach a final state which may be regarded as one of internal thermal equilibrium. Such a final state is one of spatial uniformity or homogeneity of temperature. The existence of such states is a basic postulate of classical thermodynamics. This postulate is sometimes, but not often, called the minus first law of thermodynamics. A notable exception exists for isolated quantum systems which are many-body localized and which ''never'' reach internal thermal equilibrium.Thermal contact
Heat can flow into or out of aBodies prepared with separately uniform temperatures, then put into purely thermal communication with each other
If bodies are prepared with separately microscopically stationary states, and are then put into purely thermal connection with each other, by conductive or radiative pathways, they will be in thermal equilibrium with each other just when the connection is followed by no change in either body. But if initially they are not in a relation of thermal equilibrium, heat will flow from the hotter to the colder, by whatever pathway, conductive or radiative, is available, and this flow will continue until thermal equilibrium is reached and then they will have the same temperature. One form of thermal equilibrium is radiative exchange equilibrium. Prevost, P. (1791)Change of internal state of an isolated system
If an initially isolated physical system, without internal walls that establish adiabatically isolated subsystems, is left long enough, it will usually reach a state of thermal equilibrium in itself, in which its temperature will beIn a gravitational field
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. 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. Considerations of kinetic theory or statistical mechanics also support this statement.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. 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. 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."Eu, B.C. (2002). ''Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics'', Kluwer Academic Publishers, Dordrecht, , page 13.Thermal equilibrium of planets
A planet is in thermal equilibrium when the incident energy reaching it (typically the solar irradiance from its parent star) is equal to theSee also
* Thermodynamic equilibrium * Radiative equilibrium *Citations
Citation references
*Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, McGraw-Hill, London, . *Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN, 0-88318-797-3. * Boltzmann, L. (1896/1964). ''Lectures on Gas Theory'', translated by S.G. Brush, University of California Press, Berkeley. * Chapman, S., Cowling, T.G. (1939/1970). ''The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases'', third edition 1970, Cambridge University Press, London. * Gibbs, J.W. (1876/1878). On the equilibrium of heterogeneous substances, ''Trans. Conn. Acad.'', 3: 108-248, 343-524, reprinted in ''The Collected Works of J. Willard Gibbs, Ph.D, LL. D.'', edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp. 55–353. * Maxwell, J.C. (1867). On the dynamical theory of gases, ''Phil. Trans. Roy. Soc. London'', 157: 49–88. *Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London. * Partington, J.R. (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green and Co., London. * Planck, M., (1897/1903)