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The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. Two systems are said to be in the relation of thermal equilibrium if they are linked by a wall permeable only to heat, and do not change over time.〔Carathéodory, C. (1909).〕 As a convenience of language, systems are sometimes also said to be in a relation of thermal equilibrium if they are not linked so as to be able to transfer heat to each other, but would not do so if they were connected by a wall permeable only to heat. Thermal equilibrium between two systems is a transitive relation. The physical meaning of the law was expressed by Maxwell in the words: "All heat is of the same kind".〔Maxwell, J.C. (1871), p. 57.〕 For this reason, another statement of the law is "All diathermal walls are equivalent".〔Bailyn, M. (1994), pp. 24, 144.〕 The law is important for the mathematical formulation of thermodynamics, which needs the assertion that the relation of thermal equilibrium is an equivalence relation. This information is needed for a mathematical definition of temperature that will agree with the physical existence of valid thermometers.〔Lieb, E.H., Yngvason, J. (1999), p. 56.〕 ==Zeroth law as equivalence relation== A system is said to be in thermal equilibrium when it experiences no change in its observable state (i.e. macrostate) over time. The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems.〔Lieb, E.H., Yngvason, J. (1999), p. 52.〕 In other words, the set of all equilibrated thermodynamic systems may be divided into subsets in which every system belongs to one and only one subset, and is in thermal equilibrium with every other member of that subset, and is not in thermal equilibrium with a member of any other subset. This means that a unique "tag" can be assigned to every system, and if the "tags" of two systems are the same, they are in thermal equilibrium with each other, and if they are not, they are not. Ultimately, this property is used to justify the use of thermodynamic temperature as a tagging system. Thermodynamic temperature provides further properties of thermally equilibrated systems, such as order and continuity with regard to "hotness" or "coldness", but these properties are not implied by the standard statement of the zeroth law. If it is specified that a system is in thermal equilibrium with itself (i.e., thermal equilibrium is reflexive), then the zeroth law may be stated as follows:〔Planck. M. (1914), p. 2.〕 ''If a body ''A'', be in thermal equilibrium with two other bodies, ''B'' and ''C'', then ''B'' and ''C'' are in thermal equilibrium with one another.'' This statement asserts that thermal equilibrium is a left-Euclidean relation between thermodynamic systems. If we also grant that all thermodynamic systems are in thermal equilibrium with themselves, then thermal equilibrium is also a reflexive relation. Binary relations that are both reflexive and Euclidean are equivalence relations. Thus, again implicitly assuming reflexivity, the zeroth law is therefore often expressed as a right-Euclidean statement:〔Buchdahl, H.A. (1966), p. 73.〕 ''If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.'' One consequence of an equivalence relationship is that the equilibrium relationship is symmetric: If ''A'' is in thermal equilibrium with ''B'', then ''B'' is in thermal equilibrium with ''A''. Thus we may say that two systems are in thermal equilibrium with each other, or that they are in mutual equilibrium. Another consequence of equivalence is that thermal equilibrium is a transitive relationship and is occasionally expressed as such:〔〔Kondepudi, D. (2008), p. 7.〕 ''If ''A'' is in thermal equilibrium with ''B'' and if ''B'' is in thermal equilibrium with ''C'', then ''A'' is in thermal equilibrium with ''C'' ''. A reflexive, transitive relationship does not guarantee an equivalence relationship. In order for the above statement to be true, ''both'' reflexivity ''and'' symmetry must be implicitly assumed. It is the Euclidean relationships which apply directly to thermometry. An ideal thermometer is a thermometer which does not measurably change the state of the system it is measuring. Assuming that the unchanging reading of an ideal thermometer is a valid "tagging" system for the equivalence classes of a set of equilibrated thermodynamic systems, then if a thermometer gives the same reading for two systems, those two systems are in thermal equilibrium, and if we thermally connect the two systems, there will be no subsequent change in the state of either one. If the readings are different, then thermally connecting the two systems will cause a change in the states of both systems and when the change is complete, they will both yield the same thermometer reading. The zeroth law provides no information regarding this final reading. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Zeroth law of thermodynamics」の詳細全文を読む スポンサード リンク
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