# Thermodynamics

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## Pressure dependence

In contrast to liquid and solid volumes, gas volumes are highly pressure-dependent. Since the change in volume is also associated with a change in concentration, the position of gas equilibria is often pressure-dependent.

The equilibrium constant of the reaction:

$N2O4(G)⇌2NO2(G)$

is at 117 $° C$ K = 1 $molL.-1$. First of all, the equilibrium concentrations are to be calculated, which result from an initial concentration [N2O4]0 = 1 $molL.-1$ form:

$K=[NO2]2[N2O4][NO2]=xK=x21molL.-1−x2x=[NO2]=0,781[N2O4]=1molL.-1−x2=0,61$

The ratio [NO2] / [N2O4] is then 1.35.

If the pressure is reduced to half, the volume doubles and the concentrations of the substances are initially halved. The equilibrium condition is then not fulfilled because the reduction in concentration has a greater effect in the numerator than in the denominator of the law of mass action. Accordingly, it has to be as long as2O4 to NO2 dissociate until the fraction has the value 1 again.

Immediately after the pressure reduction, the following new initial concentrations are available:

$[NO2]0=0,4molL.-1 and [N2O4]0=0,3molL.-1.$

After the equilibrium has been re-established, a mol / l is NO2 newly formed and a / 2 mol N2O4 disappeared:

$K =(0,4molL.-1+a)2(0,3molL.-1−a2)=1molL.-1$

Solving the quadratic equation gives a = 0.1 mol / l. For the concentrations present in the newly set equilibrium one obtains:

$[NO2]=0,4molL.-1 + 0,1molL.-1=0,5molL.-1[N2O4]=0,3molL.-1+ 0,05molL.-1=0,35molL.-1$

The ratio [NO2] / [N2O4] by lowering the pressure from 1.35 to 2.0 in favor of NO2 postponed.

The qualitative consequences are obvious: reactions that take place with an increase in the total amount of gas are shifted to the left by increasing the pressure and to the right by reducing the pressure. The opposite applies to reactions that take place with a decrease in the total amount of gas. According to Le Chatelier, the system evades an increase in pressure by taking up a smaller volume, and a decrease in pressure by generating a larger number of gas molecules.

For example, technical ammonia production is carried out under increased pressure (several 100 bar) to increase the yield:

$N2(G)+3H2(G)⇌2NH3(G).$

If the total amount of gas does not change, the equilibrium is practically non-pressure-dependent:

$H2(g) + I.2(G)⇌2HI (g).$

Equilibria, in which only condensed phases are involved, are also not dependent on pressure, if one does not consider extreme conditions in the kbar range.

A decrease in pressure corresponds to a decrease in the gas concentration. In liquid solutions, the decrease in pressure corresponds to a dilution of the solution, thus also a decrease in concentration. Dissociations that lead to an increase in the number of particles are thus favored by diluting the solution:

$I.2+ I-⇌I.3-$

Triiodide ions therefore dissociate to iodine and iodide with increasing dilution of the solution.

## Thermodynamics

thermodynamics, Branch of physics and physical chemistry that deals with statements about the properties of thermodynamic systems. The state of such a material system is clearly described by sets of parameters (state variable # 246 & # 223e). Changes in the state are associated with an exchange of energy and with the conversion of various forms of energy into one another, e.g. B. from mechanical or electrical work in heat.

I) Phenomenological or Equilibrium T.. It is a purely macroscopic scientific discipline, for which it is irrelevant that substances have a molecular structure. Material systems in thermodynamic equilibrium are examined. Experimental measurements such as temperature, pressure, volume, chem. Composition and heat capacities are used to characterize the states of equilibrium. These state variables are partially linked to one another by state functions. The T. provides quantitative statements about the energetic changes associated with changes in state (heat of reaction, heat of phase transformation), the direction and driving force of processes (affinity), the maximum useful work that can be obtained and the location of equilibria. Only qualitative statements are possible about non-equilibrium processes. The speed with which states of equilibrium are reached is not the subject of thermodynamic studies. For chem. Reactions are time-dependent in the reaction kinetics and in the T. irreversible processes (see below) investigated. Historically, the equilibrium T. first developed. The basis are the main tenets of T., which are based on experience and lead to the definition of the state parameters temperature, internal energy and entropy.

0. main clause of T.: If two bodies are in thermal equilibrium with a third, they are also in thermal equilibrium with one another. It follows from this that for macroscopic systems there is a state variable which is the same in all systems that are in equilibrium with one another. The size is the temperature T.

1st main clause of T.: It represents an extension of the law of conservation of energy in classical mechanics to include thermodynamic systems, including heat as a form of energy. The prerequisite for establishing the first law was the knowledge that heat is a form of energy and that 223 Heat and mechanical energy reciprocally in a fixed relationship, the mechanical heat equivalent, can be converted into one another (J. R. Mayer 1842). The same applies to electrical energy (J. P. Joule 1841). H. v. In 1847 Helmholtz formulated the law of the Conservation of energy, which can be seen as the general form of the 1st main clause of T.: Energy can neither be generated from nothing, nor can it be destroyed into nothing. It is only possible to convert one form of energy into another.

From this follows the impossibility of one thing Perpetual motion machine type 1, d. H. a machine that constantly emits more energy (e.g. mechanical work) than is supplied to it (e.g. in the form of heat).

Another formulation of the first law reads: In a closed system the sum of all energies is constant.

The totality of the energy supply inside the system is called internal energy U designated. Changes in internal energy are synonymous with changes in the state of the system. They can be done by exchanging heat & # 916q and / or work & # 916w with the environment according to & # 228 & # 223 & # 916U = Δw + Δq or with very small, differential changes dU = ∂w + ∂q. The sign convention in chem. Please note: Variables assigned to the system have positive signs, variables supplied by the system have negative signs. Work and heat depend on the way in which a state change takes place and are not state functions. In the differential notation, your changes are therefore denoted by & # 8706w and & # 8706q in contrast to dU designated.

Applications of the 1st law.

a) Pure homogeneous substances: In a closed system (mass m or amount of substance n is constant) the state is unambiguous through the state variables p, V and T set. These three quantities are linked by the thermal equation of state, so that it is sufficient to represent the internal energy as a function of two of these variables.

You choose U = U(T, V). Another state variable is that Enthalpy H = U + pV. For the sake of simplicity of representation, there is a dependency for them H = H(T, p) chosen.

Changes in the state variables are path-independent, i.e. total differentials: dU = (∂U/∂T)VdT + (∂U/∂V)TdV, dH = (∂H/∂T)P.dT + (∂H/∂p)Tdp. Since pure substances work only in the form of volume work dw = -p dV can exchange, dU = -p dV + ∂q and dH = dU + p dV + V dp = V dp + ∂q. From this it follows for isochore processes (V = const.) dU = ∂q, for isobaric processes (p = const.) dH = ∂q.

If heat is exchanged with its surroundings by a closed system, for processes at constant volume this is equal to the change in internal energy, for processes at constant pressure it is the same as the change in enthalpy . The following relationships can be derived for the partial differential quotients in the two total differentials: (& # 8706U/∂T)V = cV = nCV, (∂H/∂T)p = cp = nCp, (∂U/∂V)T = T(∂p/∂T)Vp, (∂H/∂p)T = VT (∂V/∂T)p. Here mean n Amount of substance, cV Heat capacity at constant volume and cp Heat capacity at constant pressure, C.V and C.p the respective molar heat capacities.

The differential quotients (& # 8706p/∂T)V and (& # 8706V/∂T)p are accessible from the thermal equation of state. So it follows e.g. B. from the ideal gas equation (i.e.U/ dV)T = 0 and (& # 8706H/∂p)T = 0 (2. Gay-Lussac's law), d. That is, the internal energy and the enthalpy of ideal gases are independent of volume or pressure. The following applies to real gases (& # 8706U/∂V)T > 0 and (& # 8706H/∂p)T > 0 (Joule-Thomson effect).

b) Two-phase systems of pure substances: The amount of substance in both phases appears as an additional variable. The functions apply U = U(T, V, n) and H = H(T, p, n) and for & # 252r H the total differential dH = (∂H/∂T)p, ndT + (∂H/∂p)T, ndp + (∂H/∂n)T, pdn. The differential quotient (& # 8706H/∂n)T, p indicates the change in enthalpy when a mole of the substance is transferred from one phase to another at constant temperature and constant pressure: (& # 8706H/∂n)T, p = ΔpH (molar phase change enthalpy, phase change heat).

c) Chem. reactions: With a chem. In reaction, the thermodynamic system contains several substances. Since the internal energy and the enthalpy are the sums of all partial energies of a system, the following applies in the ideal case U = U1 + U2 + . = Σ Ui, H = H1 + H2 + . = Σ Hi, where i denotes the index for identifying the various components. A mixture to which this additivity applies is called an ideal mixture. In real mixtures, additional interactions occur between the particles of the various components, then these additivity relationships do not apply.

For the general chem. Reaction | & # 957A.| A + | & # 957B.| B +.

νQP + & # 957P.Q +. follows & # 931 & # 957iUi = ΔR.U and & # 931 & # 957iHi= ΔR.H. Here are & # 916R.U and & # 916R.H the molar reaction energy or the molar enthalpy of reaction. The experimental determination and calculation of reaction energies and enthalpies is the subject of thermochemistry.

2nd main clause of T. (Entropy law): The 2nd law of the T. makes statements about the direction of natural processes. It defines the entropy S. as a new state variable to identify this directional dependency. There are different formulations of the 2nd main clause:

1) Heat can never be spontaneous, i.e. H. without work from outside, going from a colder to a warmer body (Clausius).

2) It is impossible to construct a periodically operating machine that does nothing more than generate mechanical work while cooling a heat reservoir (Planck and Thomson). Such an unrealizable machine becomes Perpetuum mobile II. Art called. It would be a heat engine that would continuously convert heat from a certain temperature level into usable work in a sequence of cyclical processes (periodically) taking into account the 1st law.

3) The entropy S. is a state variable # 246 & # 223e. In a closed system, the entropy can never be smaller, but only larger (in the case of irreversible processes) or remain constant (in the case of reversible processes).

In mathematical terms, the statement of the second law of thermodynamics reads dS. > 0 for volunteers, i.e. H. irreversible processes, dS. = 0 in equilibrium and with reversible processes. This only applies to closed systems. In practice, however, systems that exchange energy with the environment play an important role. In these cases, the entropy change in the environment must always be taken into account.

In chemical reactions under isothermal conditions, the enthalpy of reaction becomes & # 916R.H completely dissipated to the environment and increases its entropy by & # 916S.outside = -ΔR.H/T. The overall & # 228 change & # 916S.total of the closed system, consisting of reacting system and environment, results in & # 916S.total = ΔS.innen + ΔS.outside, with & # 916S.innen for the entropy change in the reacting system. F & # 252r & # 916S.total > 0 the process runs voluntarily.

Furthermore were the free energy F. = UTS and Gibbs free enthalpy G = HTS Are defined. These state variables have the advantage that they can be applied to closed systems without having to take into account the changes resulting from the energy exchange in the environment.

With the functions S. and G respectively. F. Can a closed formalism of the statements of the 2nd law of the T. develop.

Application of the 2nd law.

a) Pure substances: The entropy is analogous to the state variables of the 1st law, a function of p, V and T according to & # 228 & # 223 S. = f(T, V) respectively. S. = f(T, p). For example, for an ideal gas dS. = nCVd ln T + No d ln V or dS. = nCpd ln T + No d ln p.

If the system consists of two phases, then is the state function S. additionally dependent on the phase proportions: S. = f(T, p, n), whereby n indicates the amount of substance of the pure components in one of the two phases. The total differential then also contains the partial differential quotient (& # 8706S./∂n)T, p = ΔP.S.. The molar phase change entropy & # 916P.S. indicates the value by which the entropy of the substance (statistically speaking the "state of order") changes when 1 mol changes from one phase to the other. There is a connection & # 916P.S. = ΔP.H/TP., where & # 916P.H the molar enthalpy of phase change and TP. denote the temperature of the phase transition.

b) mixtures. Mixing processes, like all spontaneous processes in nature, are irreversible. The following must therefore also apply when producing an ideal mixture: & # 916S. M = S.2S.1 > 0 if S.1 the sum of the entropies of all substances before and S.2 represents the one after the mixing process. & # 916S. M is called the entropy of mixing. It applies & # 916S. M = -R & # 931 ni ln xi. Are there ni the amount of substance and xi the breakwater of the i-th component and R. the gas constant. Always there xi M> 0. The mean molar mixing functions of the internal energy U and the enthalpy H on the other hand, for ideal mixtures, & # 252r are zero (1st law).

In real mixtures, additional changes in entropy occur due to the interaction forces, which are caused by the use of the activities ai = fixi (fi = Activity coefficient) instead of the Molenbr & # 252che xi must be taken into account. Similar relationships apply to the free energy and the free enthalpy.

c) Reversible work and equilibrium conditions. Is a process with a change in enthalpy by dH connected, the maximum possible share of this energy difference can then be used as workwrev can be gained if the process & # 223 is carried out reversibly: dH = dwrev + dqrev. Every irreversible sub-step (e.g. frictional or thermal conduction component) shifts the splitting of dH to the disadvantage of the work share. The reversible work dwrev corresponds to the change dG the free enthalpy GHTS = U + pVTS or in the case of isochoric process & # 223d & # 252ration of the & # 196d changeF. of free energy F & # 8801 UTS.

Processes run voluntarily if they do work with reversible design, i. H. can be handed over to the outside (i.e.G 0) a process is then forced that does not take place spontaneously. Examples are the transfer of heat from a reservoir at a lower temperature to such a higher temperature with the addition of electrical work in the refrigerator or the charging of an accumulator. If the reversible ability to work is zero, thermodynamic equilibrium has been reached. In summary, the following criteria apply:

dG 0 & # 160voluntary processes

dG > 0, i.e.F. > 0, i.e.S. - i = Σ νiμi and & # 916S. ≡ ΔR.S. = Σ νi S - i whereby G - i, and S - i are the partial molar free energies and entropies in the reaction mixture (partial molar sizes). & # 916R.G is called the molar free enthalpy of reaction, & # 916R.S. referred to as molar reaction entropy. There is between the two sizes due to the definition of G the connection & # 916R.G = ΔR.HTΔR.S. (Gibbs-Helmholtz equation). ΔR.G is the part of the enthalpy of reaction that occurs in reversible isothermal-isobaric execution of the chem. Reaction can be gained as work. Therefore & # 916R.G even maximum useful work called. A chem. The reaction always goes voluntarily in the direction that the system for submitting useful work (& # 916R.G 0 + RT ln ai one, you get & # 916R.G = Σ νiμi 0 + Σ νiRT ln ai = ΔR.G 0 + RT Σ νi ln ai(van't Hoff's reaction isotherm), where & # 956i 0 the chem. Potential of substance i under standard conditions (i.e. in the pure state, the standard state), ai the activity of the substance i in the mixed phase and & # 916R.G 0 = Σ νiμi 0 is the standard free enthalpy of reaction.

In equilibrium, & # 916 appliesR.G = 0. This implies & # 916R.G 0 = -RT Σ νiln ai or & # 928 aiν i = e - & # 916R G 0/ RT = K. The last relation is the thermodynamic version of the law of mass action. The relationship & # 916R.G 0 = -RT ln K enables the thermodynamic calculation of equilibrium constants K from standard free enthalpies of reaction. The latter can be taken directly from thermodynamic table values ​​or using the Gibbs-Helmholtz equation & # 916R.G 0 = ΔR.H 0 – TΔR.S. 0 can be obtained.

3rd main clause of T. (Nernst's theory theorem): From numerous caloric measurements at low temperatures, Nernst concluded in 1906: When approaching the absolute zero point, the "change" goesS. the entropy of a pure substance, which is in internal equilibrium, approaches zero:

. The entropy approaches asymptotically

a constant value S.0 the zero point entropy, which can be set equal to zero by convention (Planck):

. It also follows from this:

From the point of view of the statistical interpretation of entropy S. = k ln W. (k is the Boltzmann constant, W. the thermodynamic probability) means S. = 0, since & # 223 W. = 1, i.e. This means that the system can only be arranged in one way, because all components are in the ground state (see also section on statistical thermodynamics). At very low temperatures, however, quantum effects become effective, and precise treatment is only possible with quantum statistics.

Since for & # 252r T & # 8594 0 too C.p & # 8594 0 goes, the smallest heats cause finite temperature changes. Since absolute warming is practically impossible, a system can never open T = 0 K must be cooled (set of the Absolute zero cannot be reached). In addition, the 3rd law enables the calculation of standard molar entropies of pure substances

, there S.0 = 0. Takes place in the temperature range 0 to T Phase transformations, so the phase transformation entropies must be added

Standard molar entropies are compiled in tabular values.

II) T. irreversible processes. Like the phenomenological T., this is a theory of macroscopic systems, but deals with processes in systems that are not in equilibrium. It describes quantitatively the chronological sequence of transport processes, balancing processes and chem. Reactions. A microscopic foundation of the irreversible processes is possible with the help of the non-equilibrium statistics (kinetic theory). A distinction is made between the linear and the non-linear T. irreversible processes.

1) The linear T. irreversible processes applies in the vicinity of equilibrium. Statements about the laws of chem. Reaction kinetics are only possible to a very limited extent with it, since chem. Reactions usually start far from equilibrium and the time laws are highly non-linear.

This T. characterizes a process by a Flu & # 223 J., e.g. B. a particle flow in diffusion or a heat flow in heat conduction. Cause of the flow are Powers X, d. See deviations of certain potentials or quantities proportional to them from thermodynamic equilibrium. The irreversible T. is based on three essential postulates:

a) The rivers Ji are linear of all forces Xk depending on what they cause:

. The proportionality coefficient L.ik are the transport coefficients. Examples are that 1. Fick's Law of diffusion and that Law of heat conduction.

b) In non-equilibrium states, the entropy is replaced by its temporal change, the Entropy production P = dS./ dt > 0. It is positive for every irreversible process. The system continues to develop until it has reached equilibrium. Then the entropy has reached a maximum, its change and thus also the entropy production reach the value zero. The following applies to the relationship between entropy production, forces and flows

c) When several processes are superimposed, the following applies to the transport coefficients Onsager's reciprocal relationship Lik = L.ki. For example, the coefficients of thermal diffusion and the diffusion thermal effect are equal to each other.

2) The nonlinear T. irreversible processes is still in the development stage. Since the linear relationship between forces and fluids no longer applies at a great distance from equilibrium, there is the possibility of structure formation in open, irreversible systems (dissipative structures). Questions of structure formation, stability, periodic processes and the evolution in such systems are intensively worked on, especially because of their importance for biochemistry and reaction kinetics.

III) Statistical T. Your goal is the calculation of macroscopic thermodynamic properties and state parameters from molecular data, molecular movements and interactions. It is limited to systems that are in thermodynamic equilibrium (equilibrium statistics).

Due to the large number of particles in a macroscopic system, the sizes can only be determined if methods of probability calculation and mathematical statistics are used in conjunction with a few assumptions about the molecular properties. The properties of the particles, e.g. B. location, speed or energy, are not given by discrete values ​​for each particle, but by Distribution functions described. A distribution function indicates the probability with which the corresponding property can be found in the system. The macroscopic, physically measurable quantity is then obtained through statistical averaging, i.e. H. by summation or integration via the function.

For the question of thermodynamic equilibrium, the thermodynamic probability W an important role. This is understood to mean the number of microstates through which a macrostate can be realized. The macroscopic state is the state of a macroscopic system, which is characterized by information on pressure, temperature and internal energy. Each of the possible arrangements of the individual molecules in the system is called a microstate. W. In contrast to the usual concept of probability, it is an integer and generally much greater than 1. The system strives for the macrostate with the greatest thermodynamic probability. It corresponds to the state of equilibrium. There is a connection to entropy S. = k ln W. (k is the Boltzmann constant).

One problem lies in counting the possible micro-states, since they determine the type of distribution function. In classical mechanics, the individual particles can be distinguished and placed in any number in an energy state. Exchanging two particles results in a new microstate. This type of counting provides the Boltzmann distribution. In quantum mechanics, the individual particles are indistinguishable due to the uncertainty relation. An exchange does not lead to a new microstate. Furthermore, for particles with half-integer spin (Fermions), e.g. B. electrons, the Pauli principle, d. that is, only one particle can be accommodated in an energy state. This leads to the Fermi-Dirac statistics. Particles with integer spin (Bosons), like classical particles, are possible in any number in one state. This count is called the Bose-Einstein statistic.

The partition function results in the partition function. It enables the calculation of the thermodynamic potentials, the other thermodynamic parameters and the equations of state.

## Thermodynamics

Authors: Lüdecke, Christa, Lüdecke, Dorothea

• Basics of thermodynamics explained in an understandable way
• Impulses for practical application in process engineering
• Practical learning aid through many detailed examples

• ISBN 978-3-662-58800-0
• Digitally watermarked, DRM-free
• Available formats: PDF, EPUB
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Physico-chemical basics for natural scientists and engineers in thermal process engineering

· Basics of thermodynamics explained in an understandable way

· Impetus for practical application in process engineering

· Practical learning aid through many detailed examples

· Formula collection and data collection for reference

This book introduces you to the physico-chemical field of thermodynamics
This book teaches you the physicochemical basics of thermodynamics. The authors focus on the thermodynamics of phase equilibria as the basis of thermal separation processes.
Thermodynamics is often perceived as an inaccessible and abstract branch of physics. This book provides a remedy by explaining the basics of thermodynamics in an understandable way and establishing a connection to the practical applications of thermal process engineering. Building on the theoretical foundations, the authors describe the thermodynamic properties of pure fluids and mixtures with the help of equations of state and phase diagrams. The calculation of phase equilibria and the separation of mixtures into their pure components are explained in detail.
In this way, the authors of this thermodynamics book make even complicated and complex facts easy to understand. In addition, numerous application-oriented examples and clear diagrams make it easier for you to understand.
Basics and Practical solutions in one
In this book on thermodynamics, Christa and Dorothea Lüdecke first explain important basic terms such as the main clauses and thermodynamic potentials. With this basic knowledge, you will be able to easily work out the specialist areas of the following chapters during your studies:
• Thermodynamic properties of pure fluids

• Thermodynamic properties of homogeneous mixtures

• Phase equilibria of multicomponent systems

The most important equations are of course applied after their derivation in detailed examples that help you to find independent solutions for practical problems in process engineering.
A reference work for studies and work

The most important statements of all chapters are clearly summarized in the appendix at the end of this work. This detailed summary is a repetition and an independent collection of formulas for quick reference. In addition, you will find many tables with thermodynamic data in the appendix - a useful collection for your calculations - as well as a German-English list of the terms used. All of this makes this thermodynamics book a loyal companion in basic and advanced studies right through to professional practice. It is therefore a special recommendation for:

· Students of natural sciences and process engineering

Prof. Dr. Christa Lüdecke

Prof. Dr. Dorothea Lüdecke

Christa Lüdecke studied physics and chemistry with a focus on physical chemistry, in particular thermodynamics and kinetics of solid-state reactions, and worked in research and teaching on material development, electrochemical and thermodynamic issues of energy storage and generation, and thermal process engineering during her professional activities.

Dorothea Lüdecke studied physics and chemistry with a focus on physical chemistry, especially thermodynamics, and has worked in research and teaching on reactions of semiconductors and on phase equilibria of metallic systems, aqueous and organic solutions during her professional activities.

The term  amount of particles '' is rather uncommon. Usually the term amount of substance is used. In both cases this is given in mol and has the symbol n.

The number of particles is the actual number of particles. There is no unity, at most & quot; St & uumlck & quot ;. The symbol is N.

N / n = Avogadro constant N (subscript A)

I have the formula symbol n as a concentration. say why?

What do you mean by Particle amount? This is not a technical term. Are you sure that you don't Amount of substance mean?

The number of particles is the number of particles. A drop of water contains e.g. about 1500000000000000000000 = 1.5 · middot10 & sup2 & sup1 particles.

For obvious reasons, this is a rather unwieldy statement. That is why chemists prefer to waste the amount of substance. This is simply the number of particles divided by Avogadro's constant 6.022 · middot1023 mol -1. A drop of water is approximately 0.003 mol, and so it is much more convenient to write. Nevertheless, the two statements are completely equivalent because the Avogadro constant, as a conversion factor for all substances, always has the same value under all conditions.

The state variables in thermodynamics should serve to describe a system exactly. The (macroscopic) state variables include pressure p, temperature T, volume V and the amount of substance n. One often hears the question of how many variables are needed to describe a system. There is only one unsatisfactory answer to this question, namely that the number of required state variables depends on the system (an ideal gas p · V = n · R · T needs three variables in order to be able to be clearly described).

Unfortunately, it gets a little more complicated because the state variables are still differentiated into intensive and extensive state variables. This is because there are two types of state variables: state variables that are independent of the size of the system and variables that are system-dependent. The rule here is that the extensive quantities are dependent on quantities, the intensive ones are not.

• intensive state variables are e.g. pressure and temperature.
• extensive state variables are e.g. volume and number of particles.

Example: If you add another liter of water to one liter of water (the temperature of the water is the same in both cases), the volume doubles (extensive size), but the temperature remains the same (intensive size).

The average price for classes in thermodynamics is € 19.

It depends on several factors:

• the experience and training of thermodynamics teachers
• where the course takes place (online or at home and in which city)
• the duration and number of courses

The majority of teachers offer the first lesson free of charge.

Erfahrene Privatlehrer/innen, die sich in ihrem Fachgebiet Thermodynamik auskennen, können genau da ansetzten, wo Du Hilfe benötigst und auf Deine individuellen Bedürfnisse und Ziele eingehen, was in klassischen Kursen oder in der Schule so nicht möglich ist.

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## Applications

Überkritische Fluide kombinieren das hohe Lösevermögen von Flüssigkeiten mit der niedrigen Viskosität ähnlich den Gasen. Weiterhin verschwinden sie bei Druckminderung vollständig (verdampfen). Somit eignen sie sich als ideale Lösungsmittel, welche als Nachteile lediglich den hohen Druck während des Prozesses aufweisen. Überkritische Fluide werden auch zum Erzeugen von feinsten Partikeln eingesetzt. Extraktionen mit überkritischen Fluiden werden als Destraktionen bezeichnet.

In überkritischem Wasser kann SiO2 gelöst werden. Beim Auskristallisieren am Impfkristall werden Einkristalle aus Quarz gebildet. Diese werden dann in kleine Stücke gesägt und als Schwingquarze in Quarzuhren eingesetzt.

Überkritisches Wasser löst Fette aus Fleisch heraus. Da sich viele verschiedene Substanzen im Fett ablagern, werden mit dieser Methode Medikamente und andere Substanzen aus dem Fleisch extrahiert und nachgewiesen.

Bei Textilfärbeanwendungen kann die gute Löslichkeit des Farbstoffes im überkritischen Zustand ausgenutzt werden, um den Farbstoff aufzunehmen und in die Faser zu übertragen. Nach Abschluss des Vorgangs wird die überkritische Flüssigkeit entspannt und der restliche Farbstoff fällt fest aus.

Eine Anwendung von überkritischem CO2 ist die Entkoffeinierung von Tee und Kaffee.

Mit überkritischem CO2 lassen sich biologische Präparate sehr schonend trocknen (z. B. für die Rasterelektronenmikroskopie). Dabei werden die Proben erst vernetzt, das Wasser stufenweise gegen ein Lösemittel ausgetauscht (meist Aceton) und das Aceton mit überkritischem CO2 ausgetragen. Durch diese Vorgehensweise bleiben die Strukturen weitestgehend erhalten und es treten nur wenige Artefakte auf. Das Verfahren wird Kritische-Punkt-Trocknung oder Überkritische Trocknung genannt.

## Bedeutung des 1. Hauptsatzes

Mithilfe des ersten Hauptsatzes ist es möglich, Energiebilanzen für die verschiedenen thermischen Prozesse (isotherme, isochore, isobare und adiabatische Zustandsänderungen) aufzustellen. Nähere Erläuterungen dazu sind bei den einzelnen Zustandsänderungen gegeben. Er ist auch eine entscheidende Grundlage für das Verständnis der Wirkungsweise von Wärmekraftmaschinen .
Die Bedeutung des 1. Hauptsatzes der Thermodynamik und des daraus abgeleiteten allgemeinen Prinzips von der Erhaltung der Energie geht aber weit über die Physik hinaus. Es ist heute ein Grundprinzip in allen Naturwissenschaften und fundamental für alle technischen Entwicklungen. Ist doch die Frage nach dem Wirkungsgrad einer Maschine oder eines technischen Verfahrens heute oft von entscheidender Bedeutung.
Trotz aller Bemühungen zur Verbesserung des Wirkungsgrades ist es bisher nicht gelungen, eine Maschine oder eine Vorrichtung zu bauen, die fortwährend Arbeit verrichtet, ohne dass Energie in irgendeiner Form zugeführt wird. Das Bestreben, eine solche Maschine, ein Perpetuum mobile , zu konstruieren, ist uralt. Die Vermutung dass dies unmöglich ist, führte schon 1775, mehr als 100 Jahre vor der Formulierung des Prinzips von der Energieerhaltung, zu dem Beschluss der Pariser Akademie der Wissenschaften und der Royal Society in London, keine Begutachtungen von Konstruktionen eines Perpetuum mobile mehr vorzunehmen.

Eine heute übliche Formulierung des 1. Hauptsatzes der Thermodynamik ist daher auch die über ein Perpetuum mobile:

Es ist unmöglich, eine Perpetuum mobile 1. Art zu konstruieren.

Die Bezeichnung 1. Art bezieht sich dabei auf Vorrichtungen, die im Sinne des 1. Hauptsatzes mehr äußere Arbeit verrichten als ihnen Energie zugeführt wird. Sie sind von einem Perpetuum mobile 2. Art zu unterscheiden. Nähere Erläuterungen zum Perpetuum mobile sind unter diesem Stichwort zu finden.

## Thermodynamik - Chemie und Physik

Der Abschnitt "wissen & verstehen" umfasst vier Seiten. (S. 76 - 79)

• Arbeit allgemein
• Hub-, Beschleunigungs- und Verformungsarbeit
• Leistung
• Efficiency

Der Abschnitt "forschen & anwenden" umfasst zwei Seiten mit insgesamt fünf Aufgaben:

1. Beispiele zum Rechnen
2. Die physiologische Muskelarbeit
3. Erde - Mond - Vergleich
4. Arbeitsdiagramm der Beschleunigungsarbeit
5. Motorenkennlinien

1.1 Beispiele zum Rechnen - Ergebnisse der Rechnungen:

• Kleiderschrank: W = 1 459 J h = 1,75 m
• Bergsteiger: W = 1,26 MJ
• Auto: W1 = 125 586 J W2 = 502 346 J
• Boeing 747: P = 25 000 kW (34 000 PS)

1.2 Die physiologische Muskelarbeit

Auf Play klicken, und dann auf "Schau dir dieses Video auf YouTube an"

Man wird dann auf die entsprechende YouTube-Seite weitergeleitet.

1.4 Arbeitsdiagramm der Beschleunigungsarbeit

1.3 Erde - Mond - Vergleich

1.5 Motorenkennlinien

## Zero law of thermodynamics

Das Streben nach thermischem Gleichgewicht durch Temperaturausgleich ist charakteristisch für thermodynamische Systeme. Es wird heute oft als nullter Hauptsatz der Thermodynamik bezeichnet, da diese Eigenschaft thermodynamischer Systeme Grundlage für viele Temperaturmessungen ist. Dieser Hauptsatz lautet:

Werden zwei thermodynamische Systeme (Körper) miteinander in Kontakt gebracht, so gleichen sich ihre Temperaturen in endlicher Zeit aus.

Die gleiche Temperatur bleibt auch nach der Trennung der Systeme erhalten, wenn keine Wärmeübertragung zwischen Systemen und Umgebung erfolgt.

#### Temperaturskalen

#Temperatur #Wärme #Kelvinskala #Thermometer #Celsius #Celsiusskala

#### Heat supply

#Wärme #innere Energie #Temperatur #Thermometer #Kelvin #Grad-Celsius

Die Hauptsätze der Thermodynamik sind grundlegende Erfahrungssätze, die aus zahlreichen Beobachtungen und Messungen gewonnen wurden. Der Begriff " Hauptsatz" ist ein historischer Begriff, der zunächst nur für den ersten und zweiten Hauptsatz verwendet wurde. Verknüpfen doch diese beiden Hauptsätze der Thermodynamik durch ihre Allgemeingültigkeit die verschiedenen Teilgebiete der Physik miteinander.

Für einen axiomatischen Aufbau Thermodynamik als Teildisziplin ist der Begriff des thermischen Gleichgewichts (gleiche Temperatur) von zentraler Bedeutung. Gehen doch thermodynamische Systeme nach Vorgängen, die mit Zustandsänderungen verbunden sind, nach kurzer Zeit von selbst in einen thermischen Gleichgewichtszustand über. Das bedeutet, dass die Zustandsgrößen zeitunabhängig sind. Dieses Streben nach Temperaturausgleich wird daher heute oft als nullter Hauptsatz der Thermodynamik bezeichnet.

Die Temperatur wird auch nach einer Trennung der Systeme beibehalten, wenn keine Wärmeübertragung zwischen Systemen und Umgebung erfolgt.
In Bild 1 ist der typische Verlauf der Temperaturen für zwei Körper dargestellt, die sich in engem Kontakt befinden. Während sich der kältere Körper erwärmt, verringert der wärmere Körper seine Temperatur solange, bis beide Körper die gleiche Temperatur haben.