Thermodynamics

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Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies changes in heat, work, enthalpy, and entropy as related to the spontaneity of processes. At present, it designates the science of all transformations of matter and energy. The starting point for most thermodynamic considerations are the laws of thermodynamics.

Contents

Overview

Thermodynamics can be divided into two main branches.

Equilibrium thermodynamics

Equilibrium thermodynamics studies systems as they approach equilibrium. This can be done by analyzing them from the macroscopic point of view, which is the classical approach. Alternatively, they can the analyzed fro mthe microscopic perspective, which is the starting point of statistical thermodynamics.

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 term thermodynamics is usually used synonymously with equilibrium thermodynamics. A central notion for this connection is that of quasistatic processes, nmely idealized, "infinitely slow" processes. Time-dependent thermodynamic processes are studied by non-equilibrium thermodynamics.

Non-equilibrium thermodynamics

Non-equilibrium thermodynamics studies the behavior of systems far away from equilibrium. This can be done through linear or non-linear analysis of irreversible processes, allowing systems near and far away from equilibrium to be studied, respectively.

Other branches of thermodynamics

From theoretical considerations and from interactions with other research fields, over the years, other variations of thermodynamics have come into their own, such as:

History

Main article: History of thermodynamics
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It has been suggested that this article or section be merged into History of thermodynamics. (Discuss)


At its origins, thermodynamics was the study of engines. Prior to 1698 and 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, such 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.

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:

<math>S=k\log W \,</math>

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 SI-unit 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:

Mechanical parameters:
Thermal parameters:

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:

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:

  • <math>E=H-PV=A+TS</math>
  • <math>A=E-TS=G-PV</math>
  • <math>G=A+PV=H-TS</math>
  • <math>H=G+TS=E+PV</math>

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:

  • 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

Main article: 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. Examples of this include Einstein's prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes. Alternative statements that are mathematically equivalent can be given for each law.

The four laws are:

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

  • 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.
  • 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.
  • 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.
  • 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

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:

  1. You can't win.
  2. You can't break even.
  3. You can't quit the game.

Or:

  1. Zero: You must play the game
  2. First: You cannot win
  3. Second: You can't break even, except on a cold day
  4. Third: It never gets that cold

Sometimes also expressed as:

  1. There's no such thing as a free lunch.
  2. There's no lunch that's worth what you paid for it.
  3. 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

Wikibooks

References

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General subfields within physics

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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