Thermodynamics

Thermodynamics ( from Ancient Greek θερμός thermos " hot " and δύναμις dynamis "power" ), also known as thermodynamics, is a branch of classical physics. It deals with the ability to do work by redistributing energy between its various manifestations. The Basics of thermodynamics were developed from the study of volume, pressure, temperature conditions in steam engines.

A distinction is made between open thermodynamic systems, and Terminated ( isolated ). In an open system flows - as opposed to closed - Matter of the system boundary, closed systems are also energy dense. According to the energy conservation law is the sum of all forms of energy ( thermal, chemical, spring tension, magnetization, etc. ) remains constant.

The thermodynamics brings the process variables and heat work on the system boundary with the state variables in the context, which describe the state of the system. Distinction is made between intensive state variables (such as temperature T, pressure p, n concentration and the chemical potential μ ) and extensive state variables ( for example, internal energy U, entropy S, volume V and particle number N ) differed.

On the basis of four fundamental main clauses as well as material-specific, empirical equations of state between the state variables (see, eg gas law ) allows the thermodynamics through the establishment of equilibrium conditions statements about which changes to a system are possible ( for example, can run what chemical reactions, phase transitions, but not like ) and the values ​​of the intensive state variables are needed for that. It is used for calculation of vacant thermal energy, pressure, temperature or volume changes, and therefore has great significance for the understanding and planning of processes in chemical plants, in heat engines as well as heating and air conditioning.

However, the thermodynamics makes no claims about how fast the processes occur (kinetics ), so it was an effort to replace the term thermodynamics by thermal statics.

Due to the statistical mechanics by James Clerk Maxwell and Ludwig Boltzmann many aspects of thermodynamics based on microscopic theories can be confirmed. Throughout its presentation, however, it continues to retain the excellent status of an independent physical theory. However, their applicability must be suitably restricted systems, namely those which are derived from a sufficient number of individual systems, so most particles composed.

• 5.1 The various statements
• 5.2 Examples
• 5.3 Summary of the statements of the second law
• 5.4 validity

History

The French physicist Nicolas Léonard Sadi Carnot studied the quantities of heat of a steam engine (1824 ). He noted that hot steam heated for cooler water reservoir and mechanical work is done. Carnot assumed that no heat is lost in this process. Carnot described the processes in the steam engine as a circular process, which was shown in later years by Émile Clapeyron in mathematical form ( Carnot cycle ).

The German physician Julius Robert Mayer formulated (1841 ) the theory that energy should be a constant size in a closed system. Energy can not disappear, but only be converted into a different form. This realization is known as conservation of energy. Mayer made ​​calculations for converting heat into mechanical energy. He stated how much energy corresponds to the increase in temperature of 1 gram of water by 1 ° C and calculated that this amount of energy corresponds to a mechanical energy that 1 g of matter could lift 367 feet in the air (actually 426 meters). These calculations form the basis of the First Law of Thermodynamics. James Prescott Joule certain in 1844 in more detail the mechanical equivalent of heat.

In 1840, the German -Swiss chemist Hermann Heinrich Hess published a treatise entitled Thermochemical studies based on the principle of the conservation of energy in molecules or atoms due to chemical reaction heats.

While Carnot still suspected that the amount of heat retained in full in a steam engine, Mayer took a convertibility of forms of energy to another. The German physicist Rudolf Clausius in 1854 linked the ideas of Mayer and Carnot. He showed that in the operation of a steam engine heat always flows from a warmer reservoir in a colder reservoir and thus the basic thesis of Carnot is correct. However, the heat energy is not - as assumed Carnot - constant, but it is partly converted into mechanical work. Clausius stated that the thermal energy of an engine ( steam engine ) can always be transformed only partially into mechanical work; the other part of the energy is dissipated to the environment. The efficiency of an engine is at the conversion ratio obtained by mechanical energy supplied to the heat. Clausius knowledge forms the Second Law of Thermodynamics: " There is no cyclically operating functioning machine that does nothing to transform the heat into mechanical work. " The amount of heat that can not be used for mechanical work is dissipated to the environment. This is not useable heat Clausius linked with the corresponding temperature to a new function, the entropy. All natural energy conversion processes contain an irreversible entropic contribution, is delivered at the unused heat to the environment. Entropy means an " inward-looking, that is no longer, convertible or usable energy. " Later Boltzmann summed up, quite clearly, the entropy as a measure of the disorder of the movements of a system. Only in a closed system and a reversible change of state is the entropy difference between initial and final states is zero.

The French chemist Marcelin Berthelot took as a driving force for a chemical reaction, thereby developing heat to (1862 ).

Hermann Helmholtz linked in batteries the electrical energy to the chemical energy and the thermal energy. He developed in his treatise Concerning the conservation of force, regardless of Mayer conservation of energy.

Helmholtz dealt in later years with energy issues in chemical reactions. Helmholtz gave Berthelot right that in many chemical transformations, heat is released; there was, however, conversions where cold is generated. Helmholtz divided in his treatise The thermodynamics of chemical processes in the energy transformations in free and bound energy. The internal energy and the Helmholtz free energy associated with the product of entropy and temperature. Transformations are only possible after Helmholtz, if the free energy decreases. The American physical chemist Josiah Willard Gibbs came almost simultaneously 1875-1878 to similar considerations as Helmholtz. The relationship between enthalpy minus the product of entropy and temperature is defined as the difference in Gibbs energy. The relationship is, in honor of the two scientists Gibbs - Helmholtz equation. With this equation, the chemist can make statements about a material realization of molecules. It can calculate the required temperatures and concentrations of chemical reactions.

In addition to the classical thermodynamics, the kinetic theory of gases was developed. Gases consist then of particles atoms or molecules that move between relatively rare collisions freely in empty space. Increasing the temperature, the particles move faster and exert frequent and more violent shocks increasing the pressure on the vessel walls from. Important representatives of this theory were Krönig August (1822-1879), Rudolf Clausius, James Clerk Maxwell and Ludwig Boltzmann. Maxwell and Boltzmann used the theory of probability to describe thermodynamic quantities on a molecular basis.

In 1999, an axiomatic system was introduced by physicists Elliott Lieb and Jakob Yngvason, in which the definition of entropy is based on the concept of adiabatic accessibility and stands on a strictly mathematical basis in the form of 15 axioms. The temperature is only a derivative of the entropy as basic variable size.. The concept of adiabatic accessibility is based on an axiomatic justification of Constantin Carathéodory in 1909, since this theory to the results has no effect, it has in practice been no - only in exceptional cases and in the teaching - found entrance.

Due to the relatively long history of the thermodynamics and broad application areas use the descriptions in the technical thermodynamics ( for example in the description of an internal combustion engine or a refrigerator ), the chemical thermodynamics (e.g., in the description of a chemical reaction ), and the statistical thermodynamics (eg in the description of correlated quantum states in solids ) are often significantly different formalisms.

Brief summary of the main theorems

0 Law: Introduction of temperature as a basic physical parameter: If two systems each with a third in thermodynamic equilibrium, they are also among each other in balance. That state quantity coincides with these systems is the temperature.

1st law: The energy of an isolated system is constant.

2nd law: Thermal energy is not convertible to any extent in other types of energy.

3rd Law: The absolute zero temperature is unattainable.

" Zeroth " law

If a system A, there is a system B and B with a system C is in thermal equilibrium, then also A is in thermal equilibrium with C. The state quantity, which corresponds, in these systems, is the temperature.

In other words, the equilibrium is transitive, so two in contact systems have exactly the same temperature then when they are in thermal equilibrium, ie, when no heat is exchanged between them (more).

For example, a thermometer itself is a system and is to be referred to as B. If B indicates the same temperature for a system A, as well as for a system C, it can be concluded that also A and C are in thermal equilibrium with each other when they are brought into contact. This law was formulated only after the three other main clauses. However, since it forms a foundation of thermodynamics, he was later referred to as " zero " main clause.

However, it is to be observed in the gravitational field that the equilibrium at different temperatures generally between the systems A, B and C, because the photons of the blackbody radiation experienced in the gravitational field due to the equivalence principle a Rot-/Blau-Verschiebung; by the time dilation they are emitted at different heights at different rates. In addition, their trajectories are curved, so that not all starting from the bottom photons arrive at the top. All of these effects cause a decrease in temperature with height. On Earth, this effect is only 1.6 × 10-14 K / m and is therefore immeasurably small. But the case of a neutron star it is not negligible.

First Law of Thermodynamics

Balance for the closed thermodynamic system

The first law of thermodynamics is derived from the set of conservation of energy: Every system has an internal energy U ( = extensive condition ). This may be W only by the transport of energy in the form of work and / or heat change Q on the boundary of the system, ie:

The infinitesimal change of the work of the system work (more precisely, the sum of the volume of work (or equivalent extensive work expressions: For example, the extensive work for a magnetic system, a magnetic field H with an increase of the magnetic moment of the sample made ​​) and in the system dissipated work, such as friction work. )

The equation is valid for the stationary system. When the moving system the external energy ( potential and kinetic energy) are added:

The energy of an isolated system remains unchanged. Various forms of energy can therefore interconvert, but energy can neither be created out of nothing, nor can it be destroyed. This is why a perpetual motion machine of the first kind is impossible ( no system performs work without supplying another form of energy and / or without reducing its internal energy ).

A limitation of convertibility of heat into work, derives from the second law of thermodynamics.

Energy balance for any open system

In the open system used, the first law is formulated mathematically different. In the open system flow over the particular system in addition to the limit mechanical work on the sliding system limit ( volume change working, for example, on the piston in a cylinder ), the displacement operation of the mass flow rates at the inlet and outlet. They are the product of pressure and volume. Instead of using the internal energy is therefore accounted for by the open system with the enthalpies that contain this term. It is:

The balance sheet for a non-stationary system in which both mass content and energy content change over time, is:

Where:

• : The time variation of the energy content in the system ( internal energy energy content = kinetic energy Potential energy).
• : The heat flow across the system boundary.
• : The working current (technical work) on the system boundary.
• : The mass flow into the system.
• : The mass flow out of the system
• : The specific enthalpy
• : The specific potential energy ( with = height above the reference level and = gravitational acceleration )
• : The specific kinetic energy ( with = speed).

Special cases and simplifications:

• Closed system: (see above)

• Stationary: and

• In addition adiabatically (eg steam turbine):

Where P is the shaft power of the machine. As delivered by the system are negative energies defined in thermodynamics, the performance of a turbine of this equation is negative. In practice, the sign is therefore switched. In simplified calculations we neglect the outer energies. Then can be at known states at inlet and outlet, the specific power directly read as Ordinatendifferenz from the hs diagram.

Energy balance for cycles

Because after passing through a cyclic process, the working medium returns to the initial state, the balance sheet, it accounts for the changes of the state variables, and process variables remain the heat and work easier. As described in connection with the second main block will be explained, not only heat can be supplied, which is completely converted into work, but it has to be removed and heat. The simple balance equation is:

Here, the circuit integral sums all heat flows. They are positive when they enter the system and negative when they leave it. is all the work of the cycle. It is negative when it is discharged.

The relationship is often written with the heat amounts:

Wherein the heat dissipation becomes more evident.

Finally, the thermal efficiency of an engine should

Still be called, the stream of benefits ( the work cycle ) in relation to the expense is ( the supplied heat, which must be usually paid in the form of fuel). The dissipated heat is usually taken from the environment.

Second Law

The second law allows the introduction of the thermodynamic entropy as a state variable for the numerical and descriptive description of processes (see Ts diagram ) and the definition of thermodynamic temperature. It restricts the statement of the first law of the equivalence of heat and work, and making it one of the foundations of thermodynamics, but is not justified in the context of this theory. Only in the context of statistical mechanics it is linked with the other theories of physics: Depending on the philosophical position he gets there, a stochastic formulation or at least a probabilistic reasoning. The word thermal radiation in observations on second law always refers to the net radiation - to Clausius ' times was understood to thermal radiation is always the net radiation. The current understanding of thermal radiation did not exist.

The various statements

The second law of thermodynamics in the formulation of Clausius is:

There is no state change, the only result is the transfer of heat from a body to a lower body elevated temperature.

In simpler terms: heat can not pass from even from a lower body temperature to a body of higher temperature. This statement seems at first to be redundant, since it corresponds to the everyday experience, as on the attraction of the earth. Nevertheless, it is equivalent to all other, less " obvious " statements, because let all contradictions to the other statements are due to a conflict with this.

The second law of thermodynamics in the formulation of Kelvin and Planck is:

"It is impossible to construct a cyclically operating machine, which brings nothing more than raising a load and cooling of a heat reservoir. "

The first law would not contradict the assumption that it is possible, one - as always kind - combustion engine supply a steady heat flow, the fully deliver these as mechanical or electrical performance. Such a machine is called a perpetual motion machine of the second kind. An appropriate formulation of the second law is:

A perpetual motion machine of the second kind is impossible.

Assuming that there is this independent of a heat sink for heat dissipation combustion engine, so therefore could be the environment, such as sea water, heat can be extracted and converted into mechanical work. One could thus remove the heat from a reservoir or tank and drive with the converted energy a heat pump, which promotes heat from another vessel at a lower temperature in the former with a higher temperature with a reversible Carnot cycle and according to the picture on the right. The supplied amount of heat in the warmer container would then be greater than the power absorbed by the engine, because the output power of the heat pump consists of the sum of the recorded heat and mobility work. Heat from a colder to a hotter body ultimately flowed - If we imagine the system boundary to both machines including two heat reservoir drawn, it would be within this closed system - ie without energy and material exchange with the environment. This is a contradiction to the first statement. In principle, the same contradiction arises with the assumption that we could build an engine that has a greater efficiency than a person working with a Carnot cycle engine. This machine would be the warmer container take off less heat than the driven from their Carnot heat pump feeds there. The corresponding statement form of the second law is:

There is no heat engine that, given the moderate temperature of the heat supply and heat removal is more efficient than the formed from these temperatures Carnot efficiency.

The naming of the mean temperatures is of importance, because usually by heat supply or removal of heat, a heat reservoir changes its temperature.

Where T is any temperature (for example, not the Celsius or Fahrenheit temperature ) of the system, but by the equation of state of the "ideal gas " here, or more defined by the just- mentioned efficiency of the Carnot cycle "absolute temperature " (Kelvin).

Immediately can be formulated further in this context:

All reversible heat and power processes with the same mean temperatures of the heat supply and heat dissipation have the same efficiency as the corresponding Carnot cycle.

And:

All irreversible heat and power processes are less efficient.

The levels set in modern thermodynamics definitions (heat, work, internal energy, state variable, process size, adiabatic ...) and with the systematic classification of the systems can introduced by Clausius state variable entropy one for all closed systems and processes in open systems generally valid statement of the second law are given in mathematical form ( in open systems, the balance sheet relates to a fluid particle that moves through the system and can be considered as a closed system moving (see above) ).

This is the power dissipated within the system work ( work that does not reach to the outside, but as a result of friction, throttling or impact processes, the internal energy increases ). She is always positive. Refers to the corresponding term in the equation as " produced entropy " - in contrast to the first term, the " entropy transported " is called, and may also be negative.

For the adiabatic system, this results in:

In a closed adiabatic system can not decrease the entropy, it usually takes to. Only for reversible processes, it remains constant.

Again, the equivalence with the first statement of Clausius is easy to recognize. An automatic flow of heat from the warmer to the colder container in the above- outlined arrangement would mean that the entropy of the colder container decreases more (lower temperature T in the denominator), than that of the warmer increases, i.e., the total entropy in the system decreases, is not possible.

All spontaneously occurring processes are irreversible. There is always held an increase in entropy. Examples include the mixing of two different gases and the heat flow from a hot to a cold body without obtaining work. The restoration of the (often more "orderly " mentioned ) initial state then requires the use of energy or information (see maxwell demon shear ). Reversible processes are not associated with an increase in the total entropy and therefore not run spontaneously. Through the theoretical description of spontaneous processes running the Second Law of Thermodynamics distinguishes a direction of time, which agrees with our intuitive experience of the world ( see the example below).

With the described contexts also the following sentence is a statement of the form of the second law:

The thermal energy of a system consisting of a fraction exergy and a portion of anergy, the exergetic content disappears when the system is transferred to the ambient condition.

Exergy is convertible into other forms of energy share of thermal energy., A body or system reversibly placed on the environmental condition with a condition other than the area of the so its exergy is given as work. The heat (eg a hot flue gas in the boiler of a power plant ) delivers a body when it cools to ambient temperature can, theoretically represented by a sequence of differential Carnot processes, as in the picture on the right, used for conversion into work be. The exergetic content is obtained by summing the differential ( pink ) area fractions above the ambient temperature.

The heat sink for these processes to accommodate the anergy (blue area fraction below ) is the environment. Prevails in a gas in the initial state relative to the ambient condition is not only at a higher temperature, but also a higher pressure, there is a total exergy not only from the exergy content of the heat, but also a volume fraction work.

The thermal efficiency of real heat engine is therefore always less than 1 and - due to the default of the machine process control and the inevitable dissipative effects - also always less than the ideal heat engine:

Wherein the ambient temperature and the average temperature of heat input. It results when the yellow area of ​​the exergy is replaced by a surface equal rectangle above the line of the ambient temperature.

The Second Law therefore has significant implications. Since many machines that provide mechanical energy, they produce a detour from thermal energy ( eg diesel engine: Chemical Energy thermal energy mechanical energy ), the limitations of the second law of thermodynamics apply to their efficiencies forever. In comparison, provide hydroelectric power plants that do not require intermediate via thermal energy in the conversion, significantly higher efficiencies.

Examples

Example 1:

A force-free gas is distributed more so that it fills the available volume completely and evenly. Why this is so, it is understood if one considers the opposite case. Imagine an airtight box in weightlessness, in which moves a single particle. The probability to find this in a measurement in the left half of the box, is then exactly 1/2. If there are, however, two particles in the box, then the probability, both to be found in the left half, corresponding to only 1/ 2 x 1/2 = 1/4, and for N particles 0.5 N. The number of atoms in a gas is unimaginably high. In a volume of one cubic meter under normal pressure, it is of the order of about 3.1025 particles. The resulting probability that the gas in the box focuses spontaneously in one half, is so low that such an event will probably never happen.

How (without friction) follows the symmetry breaking macroscopic equation from the time- reversible microscopic equations of classical mechanics, is clarified in statistical mechanics. In addition, the entropy gets there a physical meaning: it is a measure of the disorder of a system or the information contained in the system. However, the Second Law loses in statistical mechanics its status as a " strictly valid " law and it is viewed as a law, in which exceptions to macroscopic levels are possible in principle, but is also unlikely that they almost never occur. Considered at the microscopic level result eg small statistical fluctuations around the equilibrium state even in closed systems mean that the entropy also slightly fluctuates around the maximum value and thereby may decrease.

Example 2:

The following example is intended to highlight the importance of the term " state" in thermodynamics and illustrate the difference of state variables and non - state variables.

We consider a sealed means of a movable piston cylinder which is filled with moles of an ideal gas. The cylinder is in thermal contact with a heat bath of temperature.

First, the system is in state 1, characterized by; thereby, the volume of the gas. A process should take given to state 2 by the system with. Temperature and amount of substance thus remain constant and the volume increases.

We discuss two different isothermal processes that do the: (1) an instantaneous expansion ( Joule- Thomson expansion ) and (2) a quasi-static expansion.

In process ( 1) the piston is "infinite" quickly pulled out (you can make the process even realize this: a vessel with a volume is divided by a removable wall into two parts, one has the bulk and is filled with ideal gas. the other portion is evacuated. the process is then passed through the extraction of the partition wall ). The gas does no work, so it is. Experimentally shows that the energy of the gas does not change ( the average rate of speed of the gas remains the same), hence the heat ( " in the form of heat energy supplied " ) is equal to zero. In summary: In Process (1 ) the energy of the initial and final state is the same. The forms of energy, work and heat disappear.

In process (2), the piston is pulled out very slowly, thereby increasing the volume. The gas does work, it is. Since the energy of the initial and final state, however, is the same (! Energy is a state variable and is independent of the litigation from ), must according to the first law in the process energy in the form of heat to be supplied. In summary: In process (2) the energy of the initial and final state ( also ) is the same. The system does work ( " loses energy in the form of work") and receives from the heat bath energy in the form of heat.

Overall, therefore, we see that the forms of energy heat and work on the concrete realization of the process depend. In thermodynamics, one uses the term for differentials of state variables and for infinitesimally small changes of non- state variables. A system having a state in a certain energy, entropy, volume, etc., but no heat or work!

Just a note: In Process (1 ) leaves the system the thermodynamic state space. The states occupied by the system between the initial and final states, are no thermodynamic equilibrium states. Therefore, the differentials are not defined in the first main theorem. However, this is also true for finite differences. The above consideration is correct for a non - quasi-static process.

Summary of the statements of the second law

Validity

The Second Law of Thermodynamics is a fact of experience dar. It is still not succeeded to prove this fundamental law of classical physics in its general validity for any macroscopic systems, starting from the basic equation of quantum theory, the many-body Schrödinger equation. This of course also applies vice versa: The Schrödinger equation is an empirical fact dar. It is still not succeeded, the general validity of this fundamental law of quantum-mechanical systems for arbitrary macroscopic systems, starting from the fundamental theorems of physics to prove (and not only of thermodynamics! ).

Regarding the validity of the second law is to distinguish between the microscopic and submicroscopic and the macroscopic range. Thus, in the Brownian motion particles can come to rest not only from the movement, but also in turn puts from rest to motion. The latter process corresponds to the conversion of heat energy into the higher kinetic energy and must be accompanied by the cooling of the environment.

Third Law

This law was proposed by Walther Nernst in 1906 and is known as the Nernst theorem. He is quantum- theoretical nature and is equivalent to the statement by the inaccessibility of the zero point of the absolute temperature:

When the temperature approaches absolute zero () the entropy is independent of thermodynamic parameters. This goes against a fixed threshold:

The constant entropy can be interpreted as represent the Boltzmann constant and the number of possible microscopic states in the ground state ( degeneracy ). For example would be for a diatomic crystal whose atoms in the ground state energy have two possible spin orientations, result.

For all physico-chemical reactions in which the participating substances are present at absolute zero as the ideal crystalline solids, the following applies:

There is only one possibility for realizing ideal solids at absolute zero.

The above statements can be proved rigorously by methods of quantum statistics.

Energy calculations in thermodynamics

The energy balance in thermodynamics has a high priority.

In a phase transition (solid-liquid - gas) or mixtures ( salt in water, a mixture of different solvents) converting energy ( enthalpy of fusion, enthalpy of vaporization, sublimation ) or transition enthalpies are required or freely in the reverse direction. When a chemical substance transformation heats of reaction or reaction enthalpies can be free or must be supplied vice versa.

For the calculation of reaction released heats at fabric reactions, the corresponding reaction equation is first set up with the appropriate stoichiometric factors. The standard enthalpies of the individual substances are listed for 25 ° C in tables. It adds the sum of the enthalpies of the products according to the stoichiometric factors and subtracts the enthalpies of the starting materials from ( Hess'scher heat rate).

The reaction or enthalpy of transition, which is delivered in a chemical reaction or phase change to the environment, has a negative sign. If necessary a power supply from the environment for a phase transition or a chemical reaction, so this has a positive sign.

The state variable is the enthalpy, in detail:

The Gibbs free energy is

By forming the total differential of the Gibbs energy and subsequent integration can be calculated if a chemical reaction is possible.

If the difference of the free energies (? G ) of the products to the starting materials ( reactants ) is negative, a phase transformation or a matter transformation is possible. If the difference in Gibbs energy of a reaction, phase change is negative, there is a reaction - if this is not kinetically inhibited - up to a point where is. The law of mass action is a special case of such a balance. If the difference in Gibbs energy is positive, a reaction or phase transformation is impossible.

In 1869, Marcellin Berthelot still believed that only chemical transformations are possible in which heat is released. Meanwhile transformations and reactions are known, in which no heat of reaction or latent heat is released. This is due to entropy

Examples:

• Upon release of Glauber's salt in water, the solution becomes colder than the surrounding area. The enthalpy is positive, however, the disorder, i.e., the entropy of the resolution to.
• Upon melting of the ice block heat in the phase transition from solid to liquid is needed. The temperature of the water does not increase, even though heat is applied from the environment. The disorder, the entropy of the molecules is in the liquid state is greater than in solid state.
• In the conversion of coal and carbon dioxide to carbon monoxide, the reaction enthalpy is positive. Due to the reaction entropy, the equilibrium measure (see: Boudouard equilibrium ) at high temperature shift to carbon monoxide.

Thermodynamics of irreversible processes

In addition to the classical equilibrium thermodynamics non- equilibrium thermodynamics or thermodynamics of irreversible processes was developed in the 20th century. For this work, the Nobel Prize in chemistry in 1968 were awarded to Lars Onsager and Ilya Prigogine 1977.

Classical thermodynamics makes non -equilibrium processes only the qualitative statement that they are not reversible, but is limited in its quantitative statements on systems that are always global in equilibrium and differ only incrementally from it. In contrast, treats the non-equilibrium thermodynamics systems that are not in a global thermodynamic equilibrium, but different. Often, however, a local thermodynamic equilibrium is still accepted.

An important result of non-equilibrium thermodynamics is the principle of minimum entropy production for open systems, which differ only slightly from the thermodynamic equilibrium. This is the area of the so-called linear irreversible thermodynamics. It describes in a unified formal framework for linear relationships between rivers and their corresponding forces. These forces are usually regarded as the gradient of a scalar quantity and the flow described by the well known linear laws of nature, such as Ohm's Law ( the current flow ), the Fick's law (diffusion), the Fourier's law (heat conduction ) and the kinetics of a chemical reaction ( reaction rate ). By accounting for the entropy, enter into the production of entropy in the system and the entropy of the system limits flowing, can be explained by the second law, the invariance of these laws show. For the example of heat conduction shows that the thermodynamics only a heat flow from the hot to the cold is compatible, and that the thermal conductivity must be a positive quantity always. By mathematical analysis it is also shown that a thermodynamic force ( for example, temperature difference or voltage difference ) in a system an additional indirect flow caused (for example, flow of electric current caused by thermal conduction ( Seebeck coefficient ), or heat flow caused by an electric current flow ( Peltier coefficient) ). By Lars Onsager was shown that the influences between rivers and not to corresponding forces is equal to ( reciprocity relations ). Since the entropy in a closed system must always be positive, add the following: The size of the cross-effects is always much smaller than the direct effects. For the example with the two forces that the cross effects ( Peltier Koeffizent and Seebeck coefficient ) of the square root of the products of the coefficients of the two direct effects corresponds to a maximum of twice ( electrical and thermal conductivity).

Deviates strongly from an open system from equilibrium, the non-linear non-equilibrium thermodynamics comes to train. An important result in this area is the Stabilititätskriterium by Ilya Prigogine and Paul Glansdorff that specifies the conditions under which the state with the minimum entropy production becomes unstable and a system may take on a more highly ordered structure with simultaneous entropy export. In this area, thus spontaneously so-called dissipative structures can develop, which have been confirmed experimentally (eg, Bénard cells). Since biological processes are to settle in this non-linear region, this result is particularly also with regard to the development of life is of great importance.

Representative

• Pierre Prévost ( Prévostscher set)
• James Prescott Joule
• Nicolas Léonard Sadi Carnot
• Julius Robert von Mayer
• Hermann von Helmholtz
• William Thomson, 1st Lord Kelvin
• James Clerk Maxwell
• Ludwig Boltzmann
• Joseph Louis Gay -Lussac
• Robert Boyle
• Edme Mariotte
• Rudolf Clausius
• Josiah Willard Gibbs
• Guillaume Amontons
• Lorenzo Romano Amedeo Carlo Avogadro
• Jacques Charles
• Ilya Prigogine