Thermodynamic temperature

Thermodynamic temperature is a measure of thermal state defined independently of any particular substance’s properties. Its absolute scale has zero at absolute zero.

Thermodynamic equilibrium: A state in which macroscopic properties remain stable and no net flows of heat or matter occur. Temperature characterizes equilibrium states and determines whether two systems exchange heat.
Carnot cycle: An ideal reversible cycle whose efficiency depends only on the temperatures of its hot and cold reservoirs. Its efficiency provides an operational route to the thermodynamic temperature scale.
Empirical temperature: A temperature scale established from reproducible readings of a chosen physical property. Unlike thermodynamic temperature, it depends initially on a particular measurement convention or material.
Ideal gas law: An equation relating pressure, volume, amount, and absolute temperature for an idealized gas. Its temperature must be absolute for the equation’s proportional relations to hold.
Entropy: A thermodynamic state function related to the number of microscopic arrangements compatible with a system’s macroscopic state. In classical thermodynamics, temperature is defined through how entropy changes with energy.
Carnot theorem: The theorem that no engine operating between two thermal reservoirs can exceed the efficiency of a reversible engine. It shows why reservoir temperature ratios can be defined without specifying a working substance.
International Temperature Scale of 1990: An internationally agreed practical scale that approximates thermodynamic temperatures using defined fixed points and instruments. It makes routine measurements practical while remaining distinct from the defining thermodynamic scale.
Boltzmann constant: The physical constant relating temperature in kelvins to energy per particle. It converts thermodynamic temperature into the energy scale used in microscopic physics.
Absolute zero: The lower limit of thermodynamic temperature, at which a system has its minimum attainable thermal energy. It anchors the absolute temperature scale at zero.
Clausius theorem: A result stating that the cyclic integral of heat divided by absolute temperature is nonpositive, with equality for reversible cycles. It underlies the thermodynamic definition of entropy and temperature.

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