平衡热力学

概览

$\displaystyle{ A = U - TS }$

$\displaystyle{ G = U - TS + PV }$

条件

• 对于一个完全孤立的系统，$\displaystyle{ S }$在热力学平衡中取最大值。
• 对于一个恒定温度和体积的系统来说，$\displaystyle{ A }$在热力学平衡中取最小值。
• 对于一个恒温恒压的系统，$\displaystyle{ G }$在热力学平衡中取最小值。

• 当两个系统的温度 Temperature相同时，它们就处于热平衡状态
• 当两个体系的压力 Pressure相同时，它们就处于力学平衡
• 当两个题体系的化学势 Chemical Potential相同时，它们就处于扩散平衡
• 所有的力 Force都是平衡的，没有明显的外部驱动力。

保留意见

J.A.贝蒂和 I.奥本海姆写道: “坚持对平衡定义的严格解释，将排除热力学应用于实际系统的所有状态。”[17]

Callen引用另一位作者的话说，他给出了“学术且严谨的论述” ，Adkins引用他的话说，他写了一本“经典著作”—— A.B.皮帕德 A.B.Pippard[18]在文中写道: “只要时间足够长，过冷水蒸汽最终会凝结，... ..。时间可能是漫长的，也许长达10100年或者更长。就大多数目的而言，只要这种迅速的变化不是人为地刺激，这些系统就可以被视为处于平衡状态。”[19]

定义

R. Haase's的热力学演示并不从对热力学平衡的限制开始，因为他打算考虑非平衡态热力学。他考虑一个具有时间不变性质的任意系统。他通过切断除外力场以外的所有外部影响来测试它的热力学平衡。如果在绝缘之后，没有任何变化，他说，系统处于平衡状态。[25]

H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡，而实际上并没有写热力学平衡一词[30]。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态，那么它将被称为处于平衡状态。”出于热力学描述的目的，Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说，只要实验测试表明‘慢’跃迁实际上是可逆的，玻璃就可以被认为处于平衡状态。”[31] 通常来说不会将这一条件作为热力学平衡定义的一部分，而是假定相反的情况：如果热力学平衡中的一个物体受到足够慢的过程的影响，则该过程可被视为足够接近可逆，并且该物体在过程中足够接近热力学平衡。[32]

A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." [20] Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.[1] This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.

M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".[33]

M.泽曼斯基 M.Zemansky还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时，系统就处于热力学平衡状态。”

P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.

P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.[34]

P.M.莫尔斯 P.M.Morse写道，热力学关注的是“热力学平衡状态”。在讨论物体与周围热源之间的热量传递时，他也使用了“热平衡”这个短语，尽管没有明确定义一个特殊的术语“热平衡”

J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".

J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".[35]

J.R. Waldram写到了“一个明确的热力学状态”。他将一个系统定义为“当其观测量随时间停止变化时”的“热平衡”。但是在这个定义之下不久，他写到一块玻璃还没有达到“完全的热力学平衡状态”。

Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.

Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.[36]

J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.

J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.[37]

J.G.柯克伍德 J.G.Kirkwood和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态，如果，在实验的时间内，(a)它强度特性与时间无关，(b)它的内部或与周围环境的边界处没有物质或能量流。”显然，他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性，并且超出了分配给实验的时间范围。他们注意到，对于两个相接触的系统，存在一个强度性质的小子类，如果这个小子类的所有子类都相等，那么所有各自的强度性质都相等。只要满足其他一些条件，热力学平衡状态可以由这个子类定义。

内部热力学平衡状态的特征

孤立系统内部热力学平衡的涨落

"系统是它自己的内部热力学平衡"的说法可能意味着"无限期地，许多这样的测量是不时进行的，在各种测量值中没有随时间变化趋势"。因此，一个系统处于它自己的内部热力学平衡，它的状态变量与它状态变量共轭函数的名义值相对应，这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微涨落期间进行的，而不是由于未知和不同的构成属性而导致的，即远离那些共轭的状态密集函数的另一组名义值。除非已知属于平衡状态的名义值，否则根据单一的度量无法进行判断。

非平衡

热力学模型

Thermodynamic models 热力学模型

• Non-random two-liquid model (NRTL model) - Phase equilibrium calculations 非随机两液模型(NRTL 模型)-相平衡计算
• UNIQUAC model - Phase equilibrium calculations UNIQUAC 模型-相平衡计算
• Time crystal 时间晶体
Topics in control theory 控制理论主题
• Steady state 稳态
• Transient state 瞬态
• Coefficient diagram method 系数图法
• Control reconfiguration 控制重构
• Cut-insertion theorem 切入定理
• Feedback 反馈
• H infinity H 无限
• Hankel singular value 汉克尔奇异值
• Krener's theorem 克雷纳定理
• Lead-lag compensator 超前滞后补偿器
• Minor loop feedback 小循环反馈
• Minor loop feedback|Multi-loop feedback 小循环反馈 | 多循环反馈
• Positive systems 正向系统
• Radial basis function 径向基底函数

Other related topics

• Root locus 根轨迹
• Signal-flow graph]]s 信号流图
• Stable polynomial 稳定多项式
• State space representation 状态空间
• Underactuation 欠驱动
• Youla–Kucera parametrization 尤拉-库切拉参数化
• Markov chain approximation method 马尔可夫链近似法

Other related topics 其他相关话题

• Automation and remote control 自动化和远程控制
• Bond graph 键合图
• Control engineering 控制工程
• Control–feedback–abort loop 控制-反馈-中止循环
• Controller (control theory) 控制器(控制理论)
• Cybernetics 控制论
• Intelligent control 智能控制
• Mathematical system theory 数学系统论
• Negative feedback amplifier 负反馈放大器
• People in systems and control 系统和控制中的人
• Perceptual control theory 知觉控制理论
• Systems theory 系统论
• Time scale calculus 时间尺度演算

General references

• Cesare Barbieri (2007) Fundamentals of Astronomy. First Edition (QB43.3.B37 2006) CRC Press ISBN|0-7503-0886-9, ISBN|978-0-7503-0886-1
• Hans R. Griem (2005) Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics), Cambridge University Press, New York,ISBN|0-521-61941-6
• C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases, Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [1]
• F. Mandl (1988) Statistical Physics, Second Edition, John Wiley & Sons

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