zeroth law of thermodynamics

　

WordNet

1. the law that if two bodies are in thermal equilibrium with a third body then the first two bodies are in thermal equilibrium with each other
2. of or relating to the null set (a set with no members)
3. a mathematical element that when added to another number yields the same number (同)0, nought, cipher, cypher
4. adjust (as by firing under test conditions) the zero of (a gun); "He zeroed in his rifle at 200 yards" (同)zero in
5. adjust (an instrument or device) to zero value
6. the sight setting that will cause a projectile to hit the center of the target with no wind blowing
7. the point on a scale from which positive or negative numerical quantities can be measured (同)zero point
8. indicating the absence of any or all units under consideration; "a zero score" (同)0
9. having no measurable or otherwise determinable value; "the goal is zero population growth"
10. indicating an initial point or origin
11. the learned profession that is mastered by graduate study in a law school and that is responsible for the judicial system; "he studied law at Yale" (同)practice of law
12. the collection of rules imposed by authority; "civilization presupposes respect for the law"; "the great problem for jurisprudence to allow freedom while enforcing order" (同)jurisprudence
13. a generalization that describes recurring facts or events in nature; "the laws of thermodynamics" (同)law of nature
14. a rule or body of rules of conduct inherent in human nature and essential to or binding upon human society (同)natural_law
15. legal document setting forth rules governing a particular kind of activity; "there is a law against kidnapping"
16. of or concerned with thermodynamics; "the thermodynamic limit" (同)thermodynamical
17. the syllable naming the sixth (submediant) note of a major or minor scale in solmization (同)lah

PrepTutorEJDIC

1. 〈U〉(アラビア数字の)『0,零』,ゼロ / 〈U〉(温度計の)『零度』;(尺度の)零位;零点 / 〈U〉無,空(くう)(nothing) / 〈U〉最下点,どん低 / 零の,ゼロの / 〈計器など〉‘を'ゼロの目盛りに合わせる
2. 〈U〉《the ~》《集合的に》(法律・法規を総称して)『法』 / 〈U〉〈C〉(個々の)『法律』,法規 / 〈U〉法の[統制]力 / 〈U〉法律学 / 〈U〉弁護士[業] / 〈U〉《the law》警察[力],警官(police) / 〈U〉法の適用(発動);訴訟(legal action) / 〈C〉(科学・芸術などでの)法則,きまり / 〈C〉〈U〉(一般に従うべき)おきて,ならわし,規則
3. 《所有・所属》…『の』,…のものである,…に属する・《材料・要素》…『でできた』,から成る・《部分》…『の』[『中の』] ・《数量・単位・種類を表す名詞に付いて》…の・《原因・動機》…『で』,のために(because of) ・《主格関係》…『の』,による,によって・《目的格関係》…『を』,の・《同格関係》…『という』・《関係・関連》…『についての』[『の』],の点で・《抽象名詞などと共に》…の[性質をもつ] ・《『It is』+『形』+『of』+『名』+『to』 doの形で,ofの後の名詞を意味上の主語として》・《分離》…『から』・《起原・出所》…『から』[『の』](out of) ・《『名』+『of』+『a』(『an』)+『名』の形で》…のような・《『名』+『of』+『mine』(『yours, his』など独立所有格)の形で》…の…・《時》(1)《副詞句を作って》…に《形容詞句を作って》…の・《時刻》《米》…前(to,《米》before)
4. 熱力学の,熱量の
5. ラ(全音階の第6音)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/08/10 11:23:08」(JST)

wiki en

[Wiki en表示]

Thermodynamics
The classical Carnot heat engine
Branches Classical Statistical Chemical Equilibrium / Non-equilibrium
Laws Zeroth First Second Third
Systems State Equation of state Ideal gas Real gas State of 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 Property diagrams Intensive and extensive properties Functions of state (Conjugate variables in italics) Temperature / Entropy Introduction to entropy Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties Process functions Work Heat
Material properties Specific heat capacity  Compressibility  Thermal expansion  Property database
Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman's thermodynamic equations Table
Potentials Free energy Free entropy Internal energy Enthalpy Helmholtz free energy Gibbs free energy
History / Culture Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics History General Heat Entropy Gas laws "Perpetual motion" machines Theories Caloric theory Vis viva Theory of heat Mechanical equivalent of heat Motive power Key publications "An Experimental Enquiry Concerning ... Heat" "On the Equilibrium of Heterogeneous Substances" "Reflections on the Motive Power of Fire" Timelines Thermodynamics Heat engines Art Maxwell's thermodynamic surface Education Entropy as energy dispersal
Scientists Bernoulli Carnot Clapeyron Clausius Carathéodory Pierre Duhem Gibbs von Helmholtz Joule Maxwell von Mayer Onsager Rankine Smeaton Stahl Thompson Thomson Waterston
Book:Thermodynamics

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then all three 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. 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". For this reason, another statement of the law is "All diathermal walls are equivalent".

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 the mathematical definition of temperature that will agree with the physical existence of valid thermometers.

Zeroth law as equivalence relation

A system is said to be in thermal equilibrium when it experiences no net change of its observable state over time. The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems. 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:

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 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. Relations that are both reflexive and Euclidean are equivalence relations. One consequence of this reasoning is that thermal equilibrium is a transitive relationship: If A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. Another consequence 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. Implicitly assuming both reflexivity and symmetry, the zeroth law is therefore often expressed as:

If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

Again, implicitly assuming both reflexivity and symmetry, the zeroth law is occasionally expressed as the transitive relationship:

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.

Foundation of temperature

The zeroth law establishes thermal equilibrium as an equivalence relationship. An equivalence relationship on a set (such as the set of thermally equilibrated systems) divides that set into a collection of distinct subsets ("disjoint subsets") where any member of the set is a member of one and only one such subset. In the case of the zeroth law, these subsets consist of systems which are in mutual equilibrium. This partitioning allows any member of the subset to be uniquely "tagged" with a label identifying the subset to which it belongs. Although the labeling may be quite arbitrary, temperature is just such a labeling process which uses the real number system for tagging. The zeroth law justifies the use of suitable thermodynamic systems as thermometers to provide such a labeling, which yield any number of possible empirical temperature scales, and justifies the use of the second law of thermodynamics to provide an absolute, or thermodynamic temperature scale. Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.

In the space of thermodynamic parameters, zones of constant temperature form a surface, that provides a natural order of nearby surfaces. One may therefore construct a global temperature function that provides a continuous ordering of states. The dimensionality of a surface of constant temperature is one less than the number of thermodynamic parameters, thus, for an ideal gas described with three thermodynamic parameters P, V and n, it is a two-dimensional surface.

For example, if two systems of ideal gases are in equilibrium, then P₁V₁/N₁ = P₂V₂/N₂ where P_i is the pressure in the ith system, V_i is the volume, and N_i is the amount (in moles, or simply the number of atoms) of gas.

The surface PV/N = const defines surfaces of equal thermodynamic temperature, and one may label defining T so that PV/N = RT, where R is some constant. These systems can now be used as a thermometer to calibrate other systems. Such systems are known as "ideal gas thermometers".

Physical meaning of the usual statement of the zeroth law

The present article states the zeroth law as it is often summarized in textbooks. Nevertheless, this usual statement perhaps does not explicitly convey the full physical meaning that underlies it. The underlying physical meaning was perhaps first clarified by Maxwell in his 1871 textbook.

In Carathéodory's (1909) theory, it is postulated that there exist walls "permeable only to heat", though heat is not explicitly defined in that paper. This postulate is a physical postulate of existence. It does not, however, as worded just previously, say that there is only one kind of heat. This paper of Carathéodory states as proviso 4 of its account of such walls: "Whenever each of the systems S₁ and S₂ is made to reach equilibrium with a third system S₃ under identical conditions, systems S₁ and S₂ are in mutual equilibrium". It is the function of this statement in the paper, not there labeled as the zeroth law, to provide not only for the existence of transfer of energy other than by work or transfer of matter, but further to provide that such transfer is unique in the sense that there is only one kind of such wall, and one kind of such transfer. This is signaled in the postulate of this paper of Carathéodory that precisely one non-deformation variable is needed to complete the specification of a thermodynamic state, beyond the necessary deformation variables, which are not restricted in number. It is therefore not exactly clear what Carathéodory means when in the introduction of this paper he writes "It is possible to develop the whole theory without assuming the existence of heat, that is of a quantity that is of a different nature from the normal mechanical quantities."

Maxwell (1871) discusses at some length ideas which he summarizes by the words "All heat is of the same kind". Modern theorists sometimes express this idea by postulating the existence of a unique one-dimensional hotness manifold, into which every proper temperature scale has a monotonic mapping. This may be expressed by the statement that there is only one kind of temperature, regardless of the variety of scales in which it is expressed. Another modern expression of this idea is that "All diathermal walls are equivalent". This might also be expressed by saying that there is precisely one kind of non-mechanical, non-matter-transferring contact equilibrium between thermodynamic systems.

These ideas may be regarded as helping to clarify the physical meaning of the usual statement of the zeroth law of thermodynamics. It is the opinion of Lieb and Yngvason (1999) that the derivation from statistical mechanics of the law of entropy increase is a goal that has so far eluded the deepest thinkers. Thus the idea remains open to consideration that the existence of heat and temperature are needed as coherent primitive concepts for thermodynamics, as expressed, for example, by Maxwell and Planck. On the other hand, Planck in 1926 clarified how the second law can be stated without reference to heat or temperature, by referring to the irreversible and universal nature of friction in natural thermodynamic processes.

History

According to Arnold Sommerfeld, Ralph H. Fowler invented the title 'the zeroth law of thermodynamics' when he was discussing the 1935 text of Saha and Srivastava. They write on page 1 that "every physical quantity must be measurable in numerical terms". They presume that temperature is a physical quantity and then deduce the statement "If a body A is in temperature equilibrium with two bodies B and C, then B and C themselves will be in temperature equilibrium with each other". They then in a self-standing paragraph italicize as if to state their basic postulate: "Any of the physical properties of A which change with the application of heat may be observed and utilised for the measurement of temperature." They do not themselves here use the term 'zeroth law of thermodynamics'. There are very many statements of these physical ideas in the physics literature long before this text, in very similar language. What was new here was just the label 'zeroth law of thermodynamics'. Fowler, with co-author Edward A. Guggenheim, wrote of the zeroth law as follows:

...we introduce the postulate: If two assemblies are each in thermal equilibrium with a third assembly, they are in thermal equilibrium with each other.

They then proposed that "it may be shown to follow that the condition for thermal equilibrium between several assemblies is the equality of a certain single-valued function of the thermodynamic states of the assemblies, which may be called the temperature t, any one of the assemblies being used as a "thermometer" reading the temperature t on a suitable scale. This postulate of the "Existence of temperature" could with advantage be known as the zeroth law of thermodynamics". The first sentence of this present article is a version of this statement. It is not explicitly evident in the existence statement of Fowler and Guggenheim that temperature refers to a unique attribute of a state of a system, such as is expressed in the idea of the hotness manifold. Also their statement refers explicitly to statistical mechanical assemblies, not explicitly to macroscopic thermodynamically defined systems.

References

Citations

Works cited

• Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 978-0-88318-797-5.
• H.A. Buchdahl (1966). The Concepts of Classical Thermodynamics. Cambridge University Press. 
• C. Carathéodory (1909). "Untersuchungen über die Grundlagen der Thermodynamik". Mathematische Annalen (in German) 67: 355–386. doi:10.1007/BF01450409.  A translation may be found here. A partly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.
• Dugdale, J. S. (1996). Entropy and its Physical Interpretation. Taylor & Francis. ISBN 0-7484-0569-0. 
• Fowler, R., Guggenheim, E.A. (1939/1965). Statistical Thermodynamics. A version of Statistical Mechanics for Students of Physics and Chemistry, first printing 1939, reprinted with corrections 1965, Cambridge University Press, Cambridge UK.
• D. Kondepudi (2008). Introduction to Modern Thermodynamics. Wiley. ISBN 978-0470-01598-8. 
• Lieb, E.H., Yngvason, J. (1999). The physics and mathematics of the second law of thermodynamics, Physics Reports, 310: 1–96.
• Maxwell, J.C. (1871). Theory of Heat, Longmans, Green, and Co., London.
• Planck. M. (1914). The Theory of Heat Radiation, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.
• Planck, M. (1926). Über die Begründing des zweiten Hauptsatzes der Thermodynamik, S.B. Preuß. Akad. Wiss. phys. math. Kl.: 453–463.
• Saha, M.N., Srivastava, B.N. (1935). A Treatise on Heat. (Including Kinetic Theory of Gases, Thermodynamics and Recent Advances in Statistical Thermodynamics), the second and revised edition of A Text Book of Heat, The Indian Press, Allahabad and Calcutta.
• Serrin, J. (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pages 3–32, in New Perspectives in Thermodynamics, edited by J. Serrin, Springer, Berlin, ISBN 3-540-15931-2.
• Sommerfeld, A. (1951/1955). Thermodynamics and Statistical Mechanics, vol. 5 of Lectures on Theoretical Physics, edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York.

Further reading

• Atkins, Peter (2007). Four Laws That Drive the Universe. New York: Oxford University Press. ISBN 978-0-19-923236-9. 

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

• 1. 民間航空機内の救急救命管理 management of inflight medical emergencies on commercial airlines
• 2. Pulse oximetry in adults
• 3. 肥満の病因 pathogenesis of obesity
• 4. スキューバダイビングの合併症 complications of scuba diving
• 5. 総胆管括約筋切開の標準手技：最前線 standard biliary sphincterotomy technique the cutting edge

English Journal

• The second laws of quantum thermodynamics.

• Brandão F1, Horodecki M2, Ng N3, Oppenheim J4, Wehner S5.
• Proceedings of the National Academy of Sciences of the United States of America.Proc Natl Acad Sci U S A.2015 Mar 17;112(11):3275-9. doi: 10.1073/pnas.1411728112. Epub 2015 Feb 9.
• The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermo
• PMID 25675476

• Consistent thermodynamic framework for interacting particles by neglecting thermal noise.

• Nobre FD1,2, Curado EM1,2, Souza AM3,2, Andrade RF4,2.
• Physical review. E, Statistical, nonlinear, and soft matter physics.Phys Rev E Stat Nonlin Soft Matter Phys.2015 Feb;91(2):022135. Epub 2015 Feb 24.
• An effective temperature θ, conjugated to a generalized entropy s(q), was introduced recently for a system of interacting particles. Since θ presents values much higher than those of typical room temperatures T≪θ, the thermal noise can be neglected (T/θ≃0) in these systems. Moreover, the con
• PMID 25768486

• Inconsistencies in steady-state thermodynamics.

• Dickman R1, Motai R1.
• Physical review. E, Statistical, nonlinear, and soft matter physics.Phys Rev E Stat Nonlin Soft Matter Phys.2014 Mar;89(3):032134. Epub 2014 Mar 27.
• We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential μ, and an effective temperature Te, are possible. μ and Te are determined via coexistence, i.e., zero fl
• PMID 24730817

Japanese Journal

• The Unique Non Self-Referential q-Canonical Distribution and the Physical Temperature Derived from the Maximum Entropy Principle in Tsallis Statistics(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

• Suyari Hiroki
• Progress of
• … The maximum entropy principle in Tsallis statistics is reformulated in the mathematical framework of the q-product, which results in the unique non self-referential q-canonical distribution. …
• NAID 110004729507

Related Links

• Thermal equilibrium

Zeroth Law of Thermodynamics The "zeroth law" states that if two systems are at the same time in thermal equilibrium with a third system, they are in thermal equilibrium with each other. If A and C are in thermal equilibrium with B ...

• Zeroth law of thermodynamicsとは - goo Wikipedia (ウィキペディア)

Wikipedia(ウィキペディア)記事検索 > [ Zeroth law of thermodynamics ] の検索結果

---

★リンクテーブル★

関連記事	「law」「zero」「thermodynamic」

「law」

　　[★]

• n.

• 法、法律

関

jurisprudence、litigation、method

　 　 　 　 　 　

「zero」

　　[★]

• n.

• ゼロ、零点

関

null

　 　 　 　 　 　 　 　 　 　

「thermodynamic」

　　[★]

• 熱力学的な

関

thermodynamically