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Thermal Equilibrium Thermal Equilibrium Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space. When the temperatures of interest are just those in the different parts of one body, the concept also requires that any flow of heat by thermal conduction or by thermal radiation into or out of one part of the body be balanced by a flow of heat in the opposite sense into or out of another part of the body. When the temperatures of interest belong to several bodies, the concept also requires that flows of heat between each pair of bodies balance to a zero net flow, but it allows the several bodies to gain or lose heat to several external reservoirs provided that their total rate of inflow from all reservoirs is equal to their total rate of outflow to all reservoirs and that each flow is unchanging in time. For some situations, the definition of transfer of heat can be problematic. Some writers use the term thermal equilibrium in a different sense. They mean by it that the spatial temperature distribution of the body is not necessarily uniform, and indeed is likely to be non-uniform, but is maintained unvarying in time, by flows of energy;

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for example they mean that there is spatially distributed radiative cooling of the body and equal and opposite spatially distributed energy addition by condensation of water vapour, just so as on average to keep the spatial distribution of temperature time-invariant. Thermal equilibrium does not mean the same as thermodynamic equilibrium, because the latter requires that there be equilibrium of all kinds, not only thermal, and that there be no flow of any kind, in the system of interest. Theoretical foundations :- It is scientifically permissible, and perhaps unavoidably necessary, to start a project of reasoning with several mutually coherent and dependent primitive presupposed concepts. The concept of thermal equilibrium is thus coherent with the concepts of temperature and of heat transfer. These three concepts hardly make physical sense without each other. They were considered coordinately before and during and after the developments of calorimetry and of thermodynamics, for example by Maxwell and by Planck Instead of relying on this triple of jointly defined physical concepts, some writers, motivated by a desire for axiomatic parsimony and precision or mathematical elegance, prefer to define thermal equilibrium by relying on a presupposed notion of thermodynamic equilibrium, in which all mechanically measurable properties of a body have become stationary, and one infers that consequently the otherwise undefined thermal properties also are stationary. CarathĂŠodory is an example of such writers, as seen in his 1909 article. This approach leaves one at the mercy of the questions of what is meant physically by "all mechanically measurable properties" and what is meant by saying that they "have become stationary", and still relying on some concept that allows bodies not 'thermally connected' to be put into 'thermal connection'. It also leaves a person, who does not know in advance the notions of heat transfer and temperature, reliant on the assumptions, such as conservation of energy, and on the mathematical development, of the theory of thermodynamics.

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Zeroth Law of Thermodynamics Examples <<-- Let us consider two beakers full of water. Then for one beaker, the temperature of water is above the normal room temperature, and for the other beaker it is below the normal room temperature. They are left on the table for some time such that they both are not in contact with each other. If we check the beakers after some time, equilibrium for both the beakers is reached. As observed both the beakers of water are at the same temperature. The two beakers actually come in thermal equilibrium with the surroundings. Hence they are in thermal equilibrium with each other also, and they are at the same temperature. <<-- When we take an electric rod and put it in water then the water also becomes hot. This is because the heat is exchanged between the two in order to come in thermal equilibrium with each other. <<-- Sweating in human body is another example. We feel a cooling effect after sweating.

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