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; 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.