Zeroth law of thermodynamics

Thermodynamics
The classical Carnot heat engine
Branches Classical Statistical Chemical Quantum thermodynamics Equilibrium / Non-equilibrium
Laws Zeroth First Second Third
Systems Closed system Open system Isolated system State Equation of state Ideal gas Real gas State of matter Phase (matter) Equilibrium Control volume Instruments Processes Isobaric Isochoric Isothermal Adiabatic Isentropic Isenthalpic Quasistatic Polytropic Free expansion Reversibility Irreversibility Endoreversibility Cycles Heat engines Heat pumps Thermal efficiency
System properties Note: Conjugate variables in italics Property diagrams Intensive and extensive properties Process functions Work Heat Functions of state Temperature / Entropy (introduction) Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties
Material properties Property databases Specific heat capacity  ${\displaystyle c=}$ ${\displaystyle T}$ ${\displaystyle \partial S}$ ${\displaystyle N}$ ${\displaystyle \partial T}$ Compressibility  ${\displaystyle \beta =-}$ ${\displaystyle 1}$ ${\displaystyle \partial V}$ ${\displaystyle V}$ ${\displaystyle \partial p}$ Thermal expansion  ${\displaystyle \alpha =}$ ${\displaystyle 1}$ ${\displaystyle \partial V}$ ${\displaystyle V}$ ${\displaystyle \partial T}$
Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman's equations Table of thermodynamic equations
Potentials Free energy Free entropy Internal energy ${\displaystyle U(S,V)}$ Enthalpy ${\displaystyle H(S,p)=U+pV}$ Helmholtz free energy ${\displaystyle A(T,V)=U-TS}$ Gibbs free energy ${\displaystyle G(T,p)=H-TS}$
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Scientists Bernoulli Boltzmann Bridgman Carathéodory Carnot Clapeyron Clausius de Donder Duhem Gibbs von Helmholtz Joule Kelvin Lewis Massieu Maxwell von Mayer Nernst Onsager Planck Rankine Smeaton Stahl Tait Thompson van der Waals Waterston
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The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized.

The zeroth law states that if two thermodynamic systems are both in thermal equilibrium with a third system, then the two systems are in thermal equilibrium with each other.^[1][2][3]

Two systems are said to be in thermal equilibrium if they are linked by a wall permeable only to heat, and they do not change over time.^[4]

Another formulation by Maxwell is "All heat is of the same kind".^[5] Another statement of the law is "All diathermal walls are equivalent".^{[6]: 24, 144}

The zeroth law is important for the mathematical formulation of thermodynamics. It makes the relation of thermal equilibrium between systems an equivalence relation, which can represent equality of some quantity associated with each system. A quantity that is the same for two systems, if they can be placed in thermal equilibrium with each other, is a scale of temperature. The zeroth law is needed for the definition of such scales, and justifies the use of practical thermometers.^[7]: 56