# Thermodynamics

Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. Thermodynamics is closely related to statistical mechanics from which many thermodynamic relationships can be derived.

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.

Thermodynamic laws are of very general validity, and 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.

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## Thermodynamic parameters

The parameters used to describe the state of a system generally depend on the exact system under consideration, and the conditions under which that system is maintained. The most commonly considered parameters are:

Mechanical parameters:
Statistical parameters:
Two more parameters can be considered for open systems:
• Number of particles, N, of each component of the system
• Chemical potential, [itex]\mu[itex], of each component of the system

The mechanical parameters listed above can be described in terms of fundamental classical or quantum physics, while the statistical parameters can be understood only in terms of statistical mechanics.

In most applications of thermodynamics, one or more of these parameters will be held constant, while one or more of the remaining parameters are allowed to vary. Mathematically, this means the system can be described as a point in n-dimensional space, where n is the number of parameters not held fixed. Using statistical mechanics, combined with the laws of classical or quantum physics, equations of state can be derived which express each of these parameters in terms of the others. The simplest and most important of these equations of state is the ideal gas law

[itex]pV=nRT[itex]

where R is the universal gas constant.

and its derived equation:

[itex]pV=NkT[itex]

where k is the Boltzmann constant.

## 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:

• [itex]E=H-PV=A+TS[itex]
• [itex]A=E-TS=G-PV[itex]
• [itex]G=A+PV=H-TS[itex]
• [itex]H=G+TS=E+PV[itex]

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 sometimes as 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.  (http://www.tpub.com/content/doe/h1012v1/css/h1012v1_94.htm)

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

Alternative statements that are mathematically equivalent can be given for each law.

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. It is stated as follows:
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.
This law is equivalent to
[itex]dU=dq+dw[itex]
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.
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. (Kelvin-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.
All processes cease as thermodynamic temperature approaches zero.
As temperature goes to 0, the entropy of a system approaches a constant.

## The laws of thermodynamics and mechanics

The First 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 F = 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.

## 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

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