Thermodynamic equilibrium

Thermodynamic equilibrium

Overview
In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

, mechanical equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

, radiative equilibrium
Radiative equilibrium
Radiative equilibrium is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of thermodynamic equilibrium. There are various types of radiative equilibrium, which is itself a kind of dynamic equilibrium....

, and chemical equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

. The word equilibrium means a state of balance. In a state of thermodynamic equilibrium, there are no net flows of matter or of energy, no phase changes
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

, and no unbalanced potentials (or driving forces), within the system. A system that is in thermodynamic equilibrium experiences no changes when it is isolated from its surroundings.

In non-equilibrium systems there are net flows of matter or energy, or phase changes are occurring; if such changes can be triggered to occur in a system in which they are not already occurring, it is said to be in a metastable equilibrium.


Classical thermodynamics deals with dynamic equilibrium
Dynamic equilibrium
A dynamic equilibrium exists once a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a steady state...

 states.
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Encyclopedia
In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

, mechanical equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

, radiative equilibrium
Radiative equilibrium
Radiative equilibrium is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of thermodynamic equilibrium. There are various types of radiative equilibrium, which is itself a kind of dynamic equilibrium....

, and chemical equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

. The word equilibrium means a state of balance. In a state of thermodynamic equilibrium, there are no net flows of matter or of energy, no phase changes
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

, and no unbalanced potentials (or driving forces), within the system. A system that is in thermodynamic equilibrium experiences no changes when it is isolated from its surroundings.

In non-equilibrium systems there are net flows of matter or energy, or phase changes are occurring; if such changes can be triggered to occur in a system in which they are not already occurring, it is said to be in a metastable equilibrium.

Overview


Classical thermodynamics deals with dynamic equilibrium
Dynamic equilibrium
A dynamic equilibrium exists once a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a steady state...

 states. The local state of a system at thermodynamic equilibrium is determined by the values of its intensive parameters, such as pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 or temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

. To be specific, thermodynamic equilibrium is characterized by the minimum of a thermodynamic potential, such as the Helmholtz free energy
Helmholtz free energy
In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume...

, i.e., systems at constant temperature and volume:
A = U – TS;


Or as the Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

, i.e., systems at constant pressure and temperature:
G = H – TS.


where T = temperature, S = entropy, U = internal energy and H = enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

. The Helmholtz free energy is often denoted by the symbol F, but the use of A is preferred by IUPAC [2].

The process that leads to a thermodynamic equilibrium is called thermalization. An example of this is a system of interacting particles that is left undisturbed by outside influences. By interacting, they will share energy/momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 among themselves and reach a state where the global statistics are unchanging in time.

Conditions for equilibrium


By considering the differential form of thermodynamic potentials
Thermodynamic potentials
A thermodynamic potential is a scalar function used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has a...

, the following relationships can be derived:
  • For a completely isolated system, ΔS = 0 at equilibrium.
  • For a system at constant temperature and volume, ΔA = 0 at equilibrium.
  • For a system at constant temperature and pressure, ΔG = 0 at equilibrium.


The various types of equilibriums are achieved as follows:
  • Two systems are in thermal equilibrium when their temperature
    Temperature
    Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

    s are the same.
  • Two systems are in mechanical equilibrium when their pressure
    Pressure
    Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

    s are the same.
  • Two systems are in diffusive equilibrium when their chemical potential
    Chemical potential
    Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...

    s are the same.
  • All forces are balanced.

Local and global equilibrium


It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 controls heat exchanges
Heat equation
The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...

. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature breaks down, and the temperature becomes undefined.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

ive particles. In a radiating
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

 gas, the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s being emitted and absorbed by the gas need not be in thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

As an example, LTE will exist in a glass of water that contains a melting ice cube
Ice cube
Ice cubes are small, roughly cube-shaped pieces of ice, conventionally used to cool beverages. Ice cubes are often preferred over crushed ice because they melt more slowly; they are standard in mixed drinks that call for ice, in which case the drink is said to be "on the rocks."Ice cubes are...

. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell-Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell-Boltzmann distribution for another temperature.

Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell-Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally stably stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Transport phenomena
Transport Phenomena
Transport Phenomena is the first textbook that is about transport phenomena. It is specifically designed for chemical engineering students...

 are processes that lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

 of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

 will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.

Thermal equilibrium


Thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

 is achieved when two systems in thermal contact
Thermal contact
In heat transfer and thermodynamics, a thermodynamic system is said to be in thermal contact with another system if it can exchange energy with it through the process of heat...

 with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.

Thermal equilibrium occurs when a system's macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

 thermal observables have ceased to change with time. For example, an ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

 whose distribution function
Distribution function
In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, f, which gives the number of particles per unit volume in phase space. It is the number of particles per unit volume having approximately the velocity near the place and time...

 has stabilised to a specific Maxwell-Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 to be attributed to the whole system. Thermal equilibrium of a system does not imply absolute uniformity within a system; for example, a river
River
A river is a natural watercourse, usually freshwater, flowing towards an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including...

 system can be in thermal equilibrium when the macroscopic temperature distribution is stable and not changing in time, even though the spatial temperature distribution reflects thermal pollution
Thermal pollution
Thermal pollution is the degradation of water quality by any process that changes ambient water temperature.A common cause of thermal pollution is the use of water as a coolant by power plants and industrial manufacturers...

inputs.

Quasistatic equilibrium


Quasistatic equilibrium is the quasi-balanced state of a thermodynamic system near to thermodynamic equilibrium, in some sense. In a quasistatic or equilibrium process, a sufficiently slow transition of a thermodynamic system from one equilibrium state to another occurs such that at every moment in time the state of the system is close to an equilibrium state. During a quasistatic process, the system reaches equilibrium much faster, almost instantaneously, than its physical parameters vary.

Non-equilibrium


Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

General references

  • Cesare Barbieri (2007) Fundamentals of Astronomy. First Edition (QB43.3.B37 2006) CRC Press ISBN 0-7503-0886-9, 9780750308861
  • 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 DC http://library.wur.nl/WebQuery/catalog/lang/1851848
  • F. Mandl (1988) Statistical Physics, Second Edition, John Wiley & Sons

External links