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第252行： − Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it. − The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform.<ref name="Planck 1914 40"/> This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers.<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref> − The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement. − + − In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.<ref name="Fitts 43"/>+ − − 为了使一个系统处于它自己的内部热力学平衡状态，它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。
→均匀温度
===均匀温度===
===均匀温度===
这种由外力引起的平衡不均匀性，对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为，“热力学最重要的概念是温度。“<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref>Planck在介绍他的论文时，简要叙述了热、温度和热平衡，然后宣布: ”在下文中，我们将主要讨论任何形式的均匀、各向同性的物体，它们的物质具有相同的温度和密度，并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样，Planck将表面效应、外场和各向异性晶体排除在外。<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> 虽然Planck提到了温度，但并没有明确提到热力学平衡的概念。相比之下，Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ，虽然没有明确地使用短语‘热力学平衡’ ，也没有明确地假设存在一个温度来定义它。
这种由外力引起的平衡不均匀性，对于强度量'''<font color="#ff8000">温度 Temperature</font>'''不会发生。'''<font color="#ff8000">E.A.古根海姆 E.A. Guggenheim</font>'''认为，“热力学最重要的概念是温度。“<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref>Planck在介绍他的论文时，简要叙述了热、温度和热平衡，然后宣布: ”在下文中，我们将主要讨论任何形式的均匀、各向同性的物体，它们的物质具有相同的温度和密度，并受到到处垂直于表面的均匀压力的作用。和Carathéodory 一样，Planck将表面效应、外场和各向异性晶体排除在外。<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> 虽然Planck提到了温度，但并没有明确提到热力学平衡的概念。相比之下，Carathéodory关于封闭系统的经典热力学演示方案假设了一个遵循 Gibbs 的“平衡态”的概念(Gibbs 经常提到一个“热力学状态”) ，虽然没有明确地使用短语‘热力学平衡’ ，也没有明确地假设存在一个温度来定义它。
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中，不存在净的内部宏观流动。特别是，这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此，包括那些非均匀外力场。对于外部施加的引力场，这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。
热力学平衡系统内的温度在时间和空间上都是均匀的。在一个处于内部热力学平衡的系统中，不存在净的内部宏观流动。特别是，这意味着系统的所有局部都处于相互辐射交换平衡。这意味着系统的温度在空间上是均匀的。这在所有情况下都是如此，包括那些非均匀外力场。对于外部施加的引力场，这可以使用拉格郎日乘子法通过变分的计算在宏观热力学术语中证明。动力学理论或统计力学也支持这种说法。<ref>Gibbs, J.W. (1876/1878), pp. 144-150.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966), pp. 127–130.</ref><ref>Münster, A. (1970), pp. 309–310.</ref><ref>Bailyn, M. (1994), pp. 254-256.</ref><ref>{{cite journal | last1 = Verkley | first1 = W.T.M. | last2 = Gerkema | first2 = T. | year = 2004 | title = On maximum entropy profiles | journal = J. Atmos. Sci. | volume = 61 | issue = 8| pages = 931–936 | doi=10.1175/1520-0469(2004)061<0931:omep>2.0.co;2| bibcode = 2004JAtS...61..931V | doi-access = free }}</ref><ref>{{cite journal | last1 = Akmaev | first1 = R.A. | year = 2008 | title = On the energetics of maximum-entropy temperature profiles | url = | journal = Q. J. R. Meteorol. Soc. | volume = 134 | issue = 630| pages = 187–197 | doi=10.1002/qj.209| bibcode = 2008QJRMS.134..187A }}</ref> Considerations of kinetic theory or statistical mechanics also support this statement.<ref>Maxwell, J.C. (1867).</ref><ref>Boltzmann, L. (1896/1964), p. 143.</ref><ref>Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 275–278.</ref><ref>{{cite journal | last1 = Coombes | first1 = C.A. | last2 = Laue | first2 = H. | year = 1985 | title = A paradox concerning the temperature distribution of a gas in a gravitational field | url = | journal = Am. J. Phys. | volume = 53 | issue = 3| pages = 272–273 | doi=10.1119/1.14138| bibcode = 1985AmJPh..53..272C }}</ref><ref>{{cite journal | last1 = Román | first1 = F.L. | last2 = White | first2 = J.A. | last3 = Velasco | first3 = S. | year = 1995 | title = Microcanonical single-particle distributions for an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 16 | issue = 2| pages = 83–90 | doi=10.1088/0143-0807/16/2/008| bibcode = 1995EJPh...16...83R }}</ref><ref>{{cite journal | last1 = Velasco | first1 = S. | last2 = Román | first2 = F.L. | last3 = White | first3 = J.A. | year = 1996 | title = On a paradox concerning the temperature distribution of an ideal gas in a gravitational field | url = | journal = Eur. J. Phys. | volume = 17 | issue = | pages = 43–44 | doi=10.1088/0143-0807/17/1/008}}</ref>
为了使一个系统处于它自己的内部热力学平衡状态，它必须处于它自己的内部热平衡状态是必要不充分的; 一个系统在到达内部热平衡之前到达内部力学平衡是可能的。<ref name="Fitts 43"/>
===Number of real variables needed for specification 规范所需的实变量数目===
===Number of real variables needed for specification 规范所需的实变量数目===