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Thermodynamics (Greek: thermos = heat and dynamis = power) is the physics of heat, work, enthalpy, and entropy changes in relation to the spontaneity of processes. In origins, thermodynamics is the study of engines. Prior to 1698, with the invention of the Savery Engine, horses were used to "power" pulleys, attached to buckets, which lifted water out of flooded salt mines in England. In the years to follow, more variations of steam engines were built; as the Newcomen Engine, and later the Watt Engine. In time, these early engines would eventually be utilized in place of horses. Thus, each engine began to be associated with a certain amount of "horse power" depending upon how many horses it had replaced! The main problem with these first engines was that they were slow and clumsy, converting less than 2% of the input fuel into useful work. In other words, large quantities of coal (or wood) had to be burned to yield only a small fraction of work output. Hence the need for a new science of engine dynamics was born.
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Overview
Thermodynamics, at present, designates the science of all transformations of matter and energy. Definitively, thermodynamics can be divided into two main branches:
- Equilibrium Thermodynamics: the study of systems as they approach equilibrium.
- Classical Thermodynamics – macroscopic analysis of systems
- Statistical Thermodynamics – microscopic analysis of systems
- Non-equilibrium Thermodynamics: the study of systems away from equilibrium.
- Near-equilibrium Thermodynamics – linear analysis of irreversible processes.
- Far-from-equilibrium Thermodynamics – nonlinear analysis of irreversible processes.
From this base, over the years, other variations of thermodynamics have come into their own as: chemical thermodynamics, thermal physics, biological thermodynamics, atmospheric thermodynamics, economic thermodynamics, environmental thermodynamics, black hole thermodynamics, and others.
While dealing with processes in which systems exchange matter or energy, classical thermodynamics is not concerned with the rate at which such processes take place, termed kinetics. For this reason, the use of the term "thermodynamics" usually refers to equilibrium thermodynamics. In this connection, a central concept in thermodynamics is that of quasistatic processes, which are idealized, "infinitely slow" processes. Time-dependent thermodynamic processes are studied by non-equilibrium thermodynamics.
History
Most cite Sadi Carnot’s 1824 paper Reflections on the Motive Power of Fire as the starting point for thermodynamics as a modern science. Carnot defined "motive power" to be the expression of the useful effect that a motor is capable of producing. Herein, Carnot introduced us to the first modern day definition of "work": weight lifted through a height. The desire to understand, via formulation, this useful effect in relation to "work" is at the core of all modern day thermodynamics.
The name "thermodynamics", however, did not arrive until some twenty-five years later when in 1849, the British mathematician and physicist William Thomson (Lord Kelvin) coined the term ‘thermodynamics' in a paper on the efficiency of steam engines. In 1850, the famed mathematical physicist Rudolf Clausius originated and defined the term enthalpy H to be the total heat content of the system, stemming from the Greek word ‘enthalpein’ meaning to warm, and defined the term entropy S to be the heat lost or turned into waste, stemming from the Greek word ‘entrepein’ meaning to turn.
In association with Clausius, in 1871, a Scottish mathematician and physicist James Clerk Maxwell formulated a new branch of thermodynamics called Statistical Thermodynamics, which functions to analyze large numbers of particles at equilibrium, i.e. systems where no changes are occurring, such that only their average properties as temperature T, pressure P, and volume V become important.
Soon thereafter, in 1875, the Austrian physicist Ludwig Boltzmann formulated a precise connection between entropy S and molecular motion:
being defined in terms of the number of possible states W such motion could occupy, where k is the Boltzmann's constant. The following year, 1876, was a seminal point in the development of human thought. During this essential period, chemical engineer Willard Gibbs, the first person in America to be awarded a PhD in engineering (Yale), published an obscure 300-pg paper titled: On the Equilibrium of Heterogeneous Substances, wherein he formulated one grand equality, the Gibbs free energy equation, which gives a measure the amount of "useful work" attainable in reacting systems.
Building on these foundations, those as Lars Onsager, Erwin Schrodinger, and Ilya Prigogine, and others, functioned to bring these engine “concepts” into the thoroughfare of almost every modern-day branch of science.
Thermodynamic parameters
The central concept of thermodynamics is that of energy, (measured in the SInit J). Energy may be transferred into a body either by compression or by heating, and extracted from a body either by expansion or by cooling. These processes make a heat engine.
So the most commonly considered thermodynamic parameters are:
- Thermal parameters:
- Temperature: T (measured in K)
- Entropy: S (measured in J K-1)
The mechanical parameters can be described in terms of classical physics, while the thermal parameters are understood in terms of statistical mechanics.
A theoretical or experimental equations of state connect these parameters. The simplest and most important of these equations of state is the ideal gas law.
Thermodynamic potentials
Four quantities, called thermodynamic potentials, can be defined in terms of the thermodynamic parameters of a physical system:
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- Internal energy E: dE=TdS - pdV
- Helmholtz free energy A: dA = −SdT - pdV
- Gibbs free energy G: dG = −SdT + Vdp
- Enthalpy H: dH = TdS + Vdp
Using the above differential forms of the four thermodynamic potentials, combined with the chain rule of product differentiation, the four potentials can be expressed in terms of each other and the thermodynamic parameters, as below:
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- E = H − PV = A + TS
- A = E − TS = G − PV
- G = A + PV = H − TS
- H = G + TS = E + PV
The above relationships between the thermodynamic potentials and the thermodynamic parameters do not depend upon the particular system being studied; they are universal relationships that can be derived using statistical mechanics, with no regard for the forces or interaction potentials between the components of the system. However, the dependence of any one of these four thermodynamic potentials cannot be expressed in terms of the thermodynamic parameters of the system without knowledge of the interaction potentials between system components, the quantum energy levels and their corresponding degeneracies, or the partition function of the system under study. However, once the dependence of one of the thermodynamic functions upon the thermodynamic variables is determined, the three other thermodynamic potentials can be easily derived using the above equations.
Thermodynamic systems
A thermodynamic system is that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the environment or surroundings (sometimes called a reservoir.) A useful classification of thermodynamic systems is based on the nature of the boundary and the flows of matter, energy and entropy through it.
There are three kinds of systems depending on the kinds of exchanges taking place between a system and its environment:
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- isolated systems: not exchanging heat, matter or work with their environment. Mathematically, this implies that TdS, dN, and pdV are all zero, and therefore dE is zero. An example of an isolated system would be an insulated container, such as an insulated gas cylinder.
- closed systems: exchanging energy (heat and work) but not matter with their environment. In this case, only dN is generally zero. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary, which can be
- adiabatic boundary: not allowing heat exchange, TdS = 0
- rigid boundary: not allowing exchange of work, pdV = 0
- open systems: exchanging energy (heat and work) and matter with their environment. A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system.
In reality, a system can never be absolutely isolated from its environment, because there is always at least some slight coupling, even if only via minimal gravitational attraction. In analyzing a system in steady-state, the energy into the system is equal to the energy leaving the system. 1
When a system is at equilibrium under a given set of conditions, it is said to be in a definite state. The state of the system can be described by a number of intensive variables and extensive variables. The properties of the system can be described by an equation of state which specifies the relationship between these variables.
The laws of thermodynamics
In Thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. This means they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer with the environment. Examples of this include Einstein's prediction of spontaneous emission around the turn of the 20th century and the current research into the thermodynamics of black holes. Alternative statements that are mathematically equivalent can be given for each law, as follows:
Zeroth law (Thermodynamic equilibrium): If systems A and B are in thermodynamic equilibrium, and systems B and C are in thermodynamic equilibrium, then systems A and C are also in thermodynamic equilibrium.
When two systems are put in contact with each other, there will be a net exchange of energy and/or matter between them unless they are in thermodynamic equilibrium. Two systems are in thermodynamic equilibrium with each other if they stay the same after being put in contact.
While this is a fundamental concept of thermodynamics, the need to state it explicitly as a law was not perceived until the first third of the 20th century, long after the first three laws were already widely in use, hence the zero numbering. There is still some discussion about its status.
Thermodynamic equilibrium includes thermal equilibrium (associated to heat exchange and parameterized by temperature), mechanical equilibrium (associated to work exchange and parameterized generalized forces such as pressure), and chemical equilibrium (associated to matter exchange and parameterized by chemical potential).
1st Law (Conservation of energy): The work exchanged in an adiabatic process depends only on the initial and the final state and not on the details of the process.
This is equivalent to a statement of the conservation of energy, because no heat flows during an adiabatic process. This means that the only energy flowing into or out of a system during an adiabatic process is work done on or by the system. The first explicit statement of the first law of thermodynamics was given by Rudolf Clausius in 1850: ‘There is a state function E, called ‘energy’, whose differential equals the work exchanged with the surroundings during an adiabatic process.’
This law is equivalent to 
where U is the internal energy of a system, Q is the heat flowing into the system, and W is the work done on the system. The energy received by the system is positive.
2nd Law (Entropy): It is impossible to obtain a process that, operating in cycle, produces no other effect than the subtraction of a positive amount of heat from a reservoir and the production of an equal amount of work. (Kelvina href="Max_Planck_ebd9.html" title="Max Planck">Planck Statement)
The entropy of a thermally isolated macroscopic system never decreases (see Maxwell's demon), however a microscopic system may exhibit fluctuations of entropy opposite to that dictated by the second law (see Fluctuation Theorem). In fact the mathematical proof of the Fluctuation Theorem from time-reversible dynamics and the Axiom of Causality, constitutes a proof of the Second Law. In a logical sense the Second Law thus ceases to be a "Law" of Physics and instead becomes a theorem which is valid for large systems or long times.
3rd Law (Absolute Zero): As temperature goes to 0, the entropy of a system approaches a constant.
It is important to remember that the laws of thermodynamics are only statistical generalizations. That is, they simply describe the tendencies of macroscopic systems. On the quantum level, the laws of thermodynamics often break down. Furthermore, as evidenced by Maxwell's demon, it is theoretically possible to specifically engineer a quantum system to break the laws of thermodynamics. The first law of thermodynamics, however, i.e. the law of conservation, has become the most sound of all laws in science. Its validity has never been disproved.
The laws of thermodynamics and mechanics
The second Law of thermodynamics is an exact consequence of the laws of mechanics—classical or quantum. The Fluctuation Theorem shows that the Second Law of Thermodynamics is also an exact consequence of the laws of mechanics except that it is only valid in the large system or long time limit.
Examples
Substances describable by temperature alone
Blackbody radiation is an example, since photon number is not conserved. Such a state is completely described by its temperature, although if phase transitions or spontaneous symmetry breaking occur other variables may be needed to discriminate among the phases. (This problem does not arise for blackbody radiation.) Given the internal energy as a function of temperature, we can define A = U - TS.
Substances describable by temperature and pressure alone
Most "pure" nonmagnetic substances fall into this category. This state is completely described by its temperature and pressure, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase. Given U and V (or the density ρ) as a function of T and P, we can define the Helmholtz energy as before and the Gibbs energy as G = U - TS + PV and the enthalpy as H = U + PV.
Substances describable by temperature, pressure and chemical potential
If there are more than one kind of atom/molecule, a substance would fall into this category. This state is completely described by its temperature, pressure and chemical potentials, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.
Substances describable by temperature and magnetic field
If a substance is a ferromagnet or a superconductor, for example, it would fall into this category. It is completely described by its temperature and magnetic field, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.
Applications of First Law of Thermodynamics
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- An Isochoric process is where the volume is held constant, meaning that the work will be zero. Additionally, any energies transferred to the system externally are transferred into internal energy. An example would be to throw a container of gas into heat. In an ideal world, the container will not expand and the gas inside will gain interal energy. In reality, the container will burst in some moment in time.
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- An Isothermal process occures at a constant temperature. In this process, the internal energy remains zero and this means that any energy transfer must equal to work.
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- An Isobaric process is held at constant pressure. An example would be to let a piston free which exerts a forces itself on a chamber of gas.
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- An Adiabatic process is when the heat change and enthalpy in a gas are equal to zero. In this case, the product of both the volume and pressure of the gas will remain constant. This means that either pressure will increase while the volume decreases or vice versa.
See also
- History of thermodynamics
- important publications in thermodynamics
- Legendre transformation
- Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics
- Statistical Mechanics
- Thermodynamic equations
- Thermodynamic properties
- Timeline of thermodynamics, statistical mechanics, and random processes
- Thermodynamics also touches upon the fields of:
- Calorimetry
- Fluid dynamics
- Phase equilibrium
- Thermal analysis
- Thermochemistry also known as chemical thermodynamics
Humor
Joke 1: “There’s as many variations of the second law of thermodynamics as there are thermodynamicists.”
Joke 2: A common scientific humor expresses the three laws simply (and surprisingly accurately) as:
- You can't win.
- You can't break even.
- You can't quit the game.
Or:
- Zero: You must play the game
- First: You cannot win
- Second: You can't break even, except on a cold day
- Third: It never gets that cold
Sometimes also expressed as:
- There's no such thing as a free lunch.
- There's no lunch that's worth what you paid for it.
- You must have lunch.
Quotes
"Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." — Albert Einstein
"In this house, we obey the laws of thermodynamics!" (after Lisa constructs a perpetual motion machine whose energy increases with time) — Homer Simpson
"The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." — Sir Arthur Eddington
External Links
- History of Thermodynamics
- Shakespeare & Thermodynamics
- Love & Thermodynamics
- Biochemistry Thermodynamics
Wikibooks
References
- Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics, W. H. Freeman Company. ISBN 0716710889
- Cengel, Yunus A.; Boles, Michael A. (2005). Thermodynamics - An Engineering Approach, McGraw-Hill. ISBN 0073107689
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Atomic, molecular, and optical physics | Classical mechanics | Condensed matter physics | Continuum mechanics | Electromagnetism | General relativity | Particle physics | Quantum field theory | Quantum mechanics | Special relativity | Statistical mechanics | Thermodynamics |
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