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
^Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 22.
^Guggenheim, E.A. (1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, North-Holland Publishing Company., Amsterdam, (1st edition 1949) fifth edition 1965, p. 8: "If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other."
^Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, Cambridge, p. 29: "... if each of two systems is in equilibrium with a third system then they are in equilibrium with each other."
^Cite error: The named reference Carathéodory-1909 was invoked but never defined (see the help page).
^Cite error: The named reference Maxwell-1871 was invoked but never defined (see the help page).
^Cite error: The named reference Bailyn-1994 was invoked but never defined (see the help page).
^Cite error: The named reference Lieb-Yngvason-1999 was invoked but never defined (see the help page).
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