Thermodynamics

thermodynamics, also as caloric theory designation, is a subsection of classical physics. It originated in in the process 19. Century on the basis of the work of James Prescott joule, Nicolas Léonard Sadi Carnot, Julius Robert ofMayer and Hermann of Helmholtz. It is the theory of the energy, its manifestation and ability to perform work. It proves as versatile applicable in chemistry, biology and technology. With its assistance one can toIt explains example why certain chemical reactions do not run off spontaneously and others. Thermodynamics is a purely macroscopic theory, which assumes the physical characteristics of a system can be described sufficiently well with macroscopic variables of state.

Intensive variables of state become, for example temperature T, pressure p and chemical Potenzial μ, of extensive variables of state, for example internal energy U, entropy S, volume V and particle number of N, differentiated. The work W and the warmth Q are not Variables of state, since they do not characterize the system in clear way at a fixed time.

The equations, the concrete connections between the variables of state for special physical systems (e.g. ideal), hot equations of state supply gas.

Thermodynamics can completely on four Axioms, which four main clauses, are developed. These axioms are in their original formulation - according to their emergence being based on empirical observations - pure experience sets. The elegant mathematical structure received thermodynamics by the work from Josiah wanting pool of broadcasting corporations Gibbs,first the meaning of the fundamental equation recognized and its characteristics formulated.

By the statistic mechanics after James Clerk Maxwell and Ludwig Boltzmann can be confirmed many aspects of thermodynamics on the basis microscopic theories. In its entire representation it keepshowever further the excellent status of an independent physical theory. Their applicability must be limited however to suitable systems, i.e. such, which of sufficient many individual systems, thus usually particles, to consist.

Table of contents

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zeroth main clause (sometimes also 4. Main clause mentioned)

if a system A with a system B as well as B with a system C in the thermal equilibrium are, then is also A with C in the thermal equilibrium.

Differently formulated, the equilibrium is transitiv. This permits it, a new variable of state to introduce the empirical temperature θ so that two systems have exactly the same temperature if them itself in the thermalEquilibrium find. This law was only formulated after the three other main clauses. Since it forms an important basis, it was designated later than zeroth main clause. It explains why a thermometer, which is located in contact with the object which can be measured,the temperature to measure can.

Instead of the temperature if the entropy is introduced not only for all thermodynamic systems, but as primary term in the phenomenological sense, then the zeroth main clause is unnecessary.

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first main clause

the first main clause of thermodynamicsis the set of the energy conservation: Each system possesses an internal energy U (=extensive variable of state). This can change only by the transport of energy in the form of work W and warmth Q over the border of the system,that means:

<math> \ qquad \ mathrm dU= \ delta Q + \ delta W< /math>

The energy of an final system remains unchanged. Different forms of energy can be converted therefore into one another, but energy cannot be produced nor destroyed neither from that anything.

In the reality goesduring a transformation always energy in the form of friction and heat exchange with the environment lost (see efficiency). Therefore a Perpetuum mobile of first kind is impossible (no system delivers work without heat exchange or change of the internal energy).

A restrictionthe commutability of warmth in work results only from the second main clause of thermodynamics.

See also: Energy equation

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second main clause

the second main clause of thermodynamics means that it an extensive variable of state entropy <math> S< /math> gives, in one final system never removes. For the change of the entropy <math> DS< /math> thus math

< \> qquad DS applies \ ge 0. </math>

Entropy is in thermodynamics a variable of state, those from the definition

< math> \ qquad dS= \ frac {\ delta Q} {T} = \ frac {\ delta Q + \ avoided \ delta Q_ {friction} \ avoided} {T} = \ frac {\ delta H - V \ delta p} {T}< /math>

over suitableSpare processes to be computed knows. The fundamental meaning of the sentence consists of the fact that it defines the thermodynamic equilibrium of final systems clearly (<math> dS=0< /math>) and concomitantly thermodynamic processes spontaneously makes running off quantifiable.

With processes spontaneously running off, which one calls also irreversibly, findsalways an entropy increase instead of. Examples are the mixture of two different gases and the heat transport from a hot to a cold body. The re-establishment (often” more arranged “mentioned) of the initial condition requires then the employment of energy or information (see Maxwell Dämon). Reversible processes are connected not with an increase of the total entropy and do not run off therefore also spontaneously.

By the theoretical description processes spontaneously running off the second main clause of thermodynamics distinguishes a direction of the time, with our intuitiveExperience world agrees.

Example:

A force-free gas distributes itself always in such a way that it fills out the volume the available completely and evenly. Why like that is, one understands, if one regards the contrary case. One places oneself an atmospheric pressure crate inthe weightlessness forwards, in which only one particle moves. The probability to find these with a measurement in the left half of the crate is then exactly 1/2. Against it if two particles are in the crate, then is the probability,to find both in the left half, only 1/2 · 1/2 = 1/4 and with N particles accordingly 0.5 N. The number of atoms in a gas is astronomically high. In a volume of a cubic meter with normal pressureit lies in the order of magnitude of approximately 10 23 particles. The probability that the gas in the crate concentrates spontaneously in a half, resulting from it, is so small that such an event will probably never occur.

As from thatthe symmetry-breaking macroscopic equation follows temporally reversible microscopic equations of the classical mechanics (without friction), in the statistic mechanics one clarifies. Besides the entropy receives a descriptive meaning there: It is a measure of the disorder of a system. However second losesMain clause in the statisischen mechanics its status as “strictly valid” law, but is regarded there as law, with which exceptions are at the same time so improbable on macroscopic levels possible in principle however that they do not occur practically. On microscopic level regardse.g. lead. and to also decrease it knows small statistic fluctuations around the equilibrium also with final systems in addition that the entropy likewise fluctuates to something around the maximum value.

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conclusions

it are possible many conclusions. Some of it are:

  1. Everythingspontaneously (in a direction) process running off are irreversible.
  2. All processes, at which friction takes place, are irreversible.
  3. Balance and mixture procedures are irreversible.
  4. Wärmekann nicht von selbst von einem Körper niedriger Temperatur auf einen Körper höherer Temperatur übergehen.In addition a compensation is necessary by other irreversible processes (z. B.Refrigerator, heat pump).
  5. The equilibrium of isolated thermodynamic systems is distinguished by a maximum principle of the entropy.
  6. Warmth can be converted not completely into work. This would be a realization one Perpetuum mobile of second kind.
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conditions

the second main clause can be proven (see Brenig, William, statistic theory of the warmth, volume 1: Equilibrium phenomena, Berlin, New York, 3. Aufl., 1992, chapter 10.2), but only under the restriction that nonelangreichweitigen reciprocal effects are present and therefore a thermodynamic system into independent subsystems to divide leave themselves, because only in this case the energies and entropies of the subsystems additive are, thus linear preservation sizes (see Brenig, William, statistic theory of the warmth, volume 1:Equilibrium phenomena, Berlin, New York, 3. Aufl., 1992, page 10).

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other formulations

in systems, which are not final, which permit thus a warming and a work transfer, apply the original formulation no more. There are, depending upon outside conditions, differentFormulations. Equivalent one for the second main clause of thermodynamics is for example the statement that with a system the free energy attached to a heating bath <math> F< /math> becomes minimal.

For example the earth is also no final system and becomes by the sun exposureand the thermal radiation in the universe constantly heated and/or. cooled.

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thermal engines

a technical aspect, which is connected with the second main clause, is the commutability of thermal energy into other forms of energy. Engineer Nicolas Léonard Sadi Carnot has for the first time investigations overthe commutability of thermal energy at steam engines made. Today the model process (carnot cycle), designated after it, supplies the theoretically maximum efficiency of a transformation of thermal energy to other forms of energy.

There thermal energy not completely into other forms of energy (z. B. River, mechanicalEnergy) to be converted can have, itself the terms Anergie and Exergie developed, which mark, which part of the thermal energy can be converted (Exergie) and which must remain as thermal energy (Anergie). It applies thereby

thermal energy = Anergie + for Exergie

and the efficiency of the material thermal engine is ever smaller or equal to that the ideal thermal engine:


<math> \ qquad \ eta = 1 - \ frac {T_ {\ rm min}} {T_ {\ rm max}} = \ frac {\ mbox {Exergie}} {\ mbox {thermal energy}},< /math>


whereby the heating baths, at which the thermal engine is attached, the temperatures <math> T_ {\ rm min}< /math>and <math> T_ {\ rm max}< /math> exhibit.


The second main clause has thus substantial technical effects. Since many machines, which supply mechanical energy, produce these over a detour from thermal energy (e.g. Diesel engine: Chemical energy <math> \ rightarrow< /math> thermal energy <math> \ rightarrow< /math> mechanical energy), apply totheir efficiencies always the restrictions 2. Main clause. In the comparison to it electric motors, which do not go during the transformation an intermediate stage over thermal energy, offer substantially higher efficiencies.


Read on to: The Second Law OF Thermodynamics (English) - a outstanding andrecreating humorous introduction of Professor. Emeritus franc L. Lambert (with resuming left on the last side)

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third main clause

this main clause was suggested from roll ago Nernst in the year 1906 and is well-known also as Nernst theorem. It is and it forbids to quantum-theoretical nature knowing a system up to the absolute zero cooling.

During the approximation of the temperature to the absolute zero (<math> T=0< /math>) the entropy becomes <math> S< /math> independently of thermodynamic parameters. Thus math <S> /math< goes> against a fixed limit value <math> S_0< /math>:


<math> \ lim_ {T \ rightarrow 0} S (T, p, V,…) = S (T=0) = S_0< /math>


The constant entropy with <math> T=0< /math> LN ( <\> Omega_0) leaves itself /math cdot as math S_0=k \< \> represent, whereby <math> k< /math> the Boltzmann constant is and <math> \ Omega_0< /math> the number of possible micro conditions in the initial state (degeneration). For example became forone <math> n< /math> - math S_0=k has atomigen crystal, its atoms in the energy initial state two <possible> spin attitudes \ cdot \ LN (2^ {n})< /math> resulted in.


To all physicochemical reactions, with which the participating materials at the absolute zero are present as ideal crystalline solids, applies:


<math> \ lim_ {T \ rightarrow 0} S (T, p…) = 0< /math>

It givesonly one realization possibility for ideal solids at the absolute zero, <math> \ Omega_0=1< /math>.

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example

the following example is the meaning of the term „condition “in thermodynamics emphasize and the difference of variables of state and non--variable of state illustrate.

We regard in addition one by means of onemobile piston final cylinder, that with <math> N_0< /math> Moles of an ideal gas is filled. The cylinder is in heat contact with a heating bath of the temperature <math> T_0< /math>.

First the system is in the condition 1, characterized through <math> (T_0, V_1, N_0)< /math>; is <math> V_1< /math> the volume of the gas. A process is the system into the condition 2 given through <math> (T_0, V_2, N_0)< /math> with <math> V_2> V_1< /math> bring. Temperature and amount of material remain thus constant and the volume become larger.

We discuss two different isotherm of processes, thosecarry out: (1) a instantane expansion (joule Thomson expansion) and (2) a quasi-static expansion.

With process (1) the piston is fast pulled out „infinitely “(one can realize the process also as follows: a container with a volume <math> V_2 </math> is by a herausnehmbare walldivided into two subranges, whereby the volume <math> V_1< /math> possesses and is filled with the ideal gas. The other subrange is evacuated. The process is then given the partition wall by pulling out). The gas does not carry a work out, it is thus <math> \ delta W = 0< /math>. Experimentally it shows up that the energy of the gas does not change (the medium speed speed of the gas particles remains directly), therefore is also the warmth („in the form of warmth supplied energy “) same zero: <math> \ delta Q =0< /math>. Summarized: With process (1) the energy of at the beginning of and final state is alike. The forms of energy work and warmth disappear.

With process (2) the piston is very slowly pulled out and thus the volume is increased. The gas carries work out, it is <math> \ deltaW < 0< /math>. Since the energy of at the beginning of and final state however the same is (the energy is a variable of state and depends not on the processing!), energy must be supplied in the form of warmth after the first main clause with the process:<math> \ delta Q = - \ delta W > 0< /math>. Summarized: With process (2) the energy of at the beginning of and final state (likewise) is alike. The system carries work out („energy loses in the form of work “) and receives from the heating bath energy in the form of warmth.

Altogether one sees thus that the forms of energy warmth and work depend on the concrete realization of the process. In thermodynamics one uses the designation <math> D< /math> for differentials of variables of state and <math> \ delta< /math> for infinitesimally small changes of non--variables of state. A system possessesin a condition a certain energy, entropy, volume, etc. but no warmth or work!

Still another note: With process (1) the system leaves the thermodynamic Zustandsraum. The conditions, which the system between at the beginning of and final state takes, are not thermodynamic equilibria.Therefore the differentials are in the 1. Main clause does not define. This applies however also to finite differences. The above view is correct also for a non-quasi-static process.

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summary

1. Main clause: In an final system the total energy is constant.

2. Main clause: There is no machine, which can convert warmth completely into other forms of energy.

3. Main clause: The absolute zero of the temperature is unattainable.

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irreversible thermodynamics

apart from classical equilibrium thermodynamics became in 20. Century the Nichtgleichgewichtsthermodynamik or also Thermodynamics of irreversible processes develops. Classical thermodynamics makes about Nichtgleichgewichtsprozesse only the qualitative statement that these are not reversible, is limited however its quantitative statements to systems, which are always global in the equilibrium, and/or. deviate only incremental from it. The gene overtreats the Nichtgleichgewichtsthermodynamik systems in a global thermodynamic equilibrium is not, but deviate from it. Often however still local thermodynamic equilibrium is accepted.

An important result of the Nichtgleichgewichtsthermodynamik is the principle of minimum entropy production for open systems, which onlyfew from the thermodynamic equilibrium deviate. This is the range of the so-called linear Nichtgleichgewichtsthermodynamik. If an open system deviates strongly from the equilibrium, the nonlinear Nichtgleichgewichtsthermodynamik comes to the course. Important result within this range is the Stabilititätskriterium of Ilya Prigogine and Paul Glansdorff, who indicates, under which conditions the condition with minimum entropy production unstably will and a system can accept a more highly arranged structure with time in accordance with entropy export. Within this range thus spontaneously so-called dissipative structures can develop, those experimentallywere confirmed (for example Bénard cells). Since in this nonlinear range also biological processes are to be settled, this result is particularly also in regard to the development of the life of great importance.

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representative

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resuming information

Wikibooks: Thermodynamics - learning and teaching materials
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of literature

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generally

  • harsh ore B. Callen: Thermodynamics and onIntroduction ton thermalstatistics. 2. Edition. Wiley text Books, New York 1985, ISBN 0-471-86256-8
  • Karl Stephan, Franz Mayinger: Thermodynamics. Bases and technical applications. 2 volumes, Springer publishing house
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chemical thermodynamics

  • Wolfgang Wagner: “Chemical thermodynamics”. 4. Edition. Academy publishing house, Berlin 1982
  • Hans Heinrich Möbius, Wolfgang Dürselen: “Chemical thermodynamics”. 5. Edition. VEB publishing house for basic industry, Leipzig 1988, ISBN 3-342-00294-8
  • Hans WernerChamber, briefly Schwabe: “Introduction to the thermodynamics of irreversible processes”. Academy publishing house Berlin, 1984
  • Hans Joachim ask-smell: “Manual of chemical thermodynamics”. Publishing house chemistry, Weinheim 1971, ISBN 3-527-25019-0
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technical thermodynamics

  • Klaus Langeheinecke, Peter Jany, Eugen Sapper: Thermodynamics for engineers.5. Edition. Vieweg publishing house, Wiesbaden 2004
  • Günter Cerbe, Gernot of William: Technical thermodynamics. Theoretical bases and practical applications. 14. Edition. Hanser technical book publishing house, June 2005, ISBN 3446402810
  • Baehr, H. - D.: “Thermodynamics”, 12.Auflage, 2 volumes
  • Elsner, N., Dittmann, A.: Bases of technical thermodynamics, Bd.1 and 2, academy publishing house, Berlin, 1993
  • Dirk Labuhn, olive Rome mountain:No panic before thermodynamics!, 1. Edition, Vieweg, Braunschweig, 2005, ISBN 3834800244
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thermodynamics in biology

  • Dieter Leuschner: Thermodynamics in biology. An introduction.AcademyPublishing house, Berlin 1989, ISBN 3-05-500487-6
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