isotemperature

Isotemperature is a term used in some branches of physics and engineering to describe a state in which the temperature is spatially uniform throughout a system. In this sense, a system with isotemperature has the same temperature at every point, typically expressed as T(r,t) = T0 for all positions r at a given time t. The term is not a standard one in core thermodynamics and is used variably in literature, often as an informal shorthand for a homogeneous temperature distribution or a thermal-equilibrium assumption.

Isotemperature is closely related to, but distinct from, isothermal processes. Isothermal describes a process that occurs at constant temperature as a function of time, whereas isotemperature emphasizes the spatial uniformity of temperature within the system. In many practical problems, assuming isotemperature is a simplification when heat transfer is fast compared to other dynamics, so the temperature field can be treated as uniform.

Examples: in a well-mixed liquid inside a conductive vessel that is in good thermal contact with a heat bath, the interior can be treated as isotemperature. In solids with high thermal conductivity and strong coupling to a heat source, gradient-free temperature fields can arise on appropriate timescales. In atmospheric or astrophysical contexts, isotemperature approximations may be used in coarse-grained models where large-scale convection enforces approximate uniformity.

Measurement and mathematics: isotemperature implies ∇T = 0 throughout the domain, and Ti = Tj for all points or components. It is an idealization rather than a universal rule and should be justified by the relative rates of heat transfer, mixing, and external forcing.