Equilibrium thermodynamics

Thermodynamics

The classical Carnot heat engine

Branches

* Classical
* Statistical
* Chemical
* Quantum thermodynamics

* Equilibrium / Non-equilibrium

Laws

* Zeroth
* First
* Second
* Third

Systems

* Closed system
* Open system
* Isolated system

|  State

* Equation of state
* Ideal gas
* Real gas
* State of matter
* Phase (matter)
* Equilibrium
* Control volume
* Instruments

Processes

* Isobaric
* Isochoric
* Isothermal
* Adiabatic
* Isentropic
* Isenthalpic
* Quasistatic
* Polytropic
* Free expansion
* Reversibility
* Irreversibility
* Endoreversibility

Cycles

* Heat engines
* Heat pumps
* Thermal efficiency

System properties

Note: Conjugate variables in italics

* Property diagrams
* Intensive and extensive properties

Process functions

* Work
* Heat

Functions of state

* Temperature / Entropy (introduction)
* Pressure / Volume
* Chemical potential / Particle number
* Vapor quality
* Reduced properties

Material properties

* Property databases

| Specific heat capacity |  c = {\displaystyle c=} | |  T {\displaystyle T} |  ∂ S {\displaystyle \partial S}

|

N {\displaystyle N} |  ∂ T {\displaystyle \partial T}
Compressibility |  β = − {\displaystyle \beta =-} | |  1 {\displaystyle 1} |  ∂ V {\displaystyle \partial V}

|

V {\displaystyle V} |  ∂ p {\displaystyle \partial p}
Thermal expansion |  α = {\displaystyle \alpha =} | |  1 {\displaystyle 1} |  ∂ V {\displaystyle \partial V}

|

V {\displaystyle V} |  ∂ T {\displaystyle \partial T}

Equations

* Carnot's theorem
* Clausius theorem
* Fundamental relation
* Ideal gas law

* Maxwell relations
* Onsager reciprocal relations
* Bridgman's equations
* Table of thermodynamic equations

Potentials

* Free energy
* Free entropy

* Internal energy
U ( S , V ) {\displaystyle U(S,V)}
* Enthalpy
H ( S , p ) = U + p V {\displaystyle H(S,p)=U+pV}
* Helmholtz free energy
A ( T , V ) = U − T S {\displaystyle A(T,V)=U-TS}
* Gibbs free energy
G ( T , p ) = H − T S {\displaystyle G(T,p)=H-TS}

* History
* Culture

|  History

* General
* Entropy
* Gas laws

* "Perpetual motion" machines

Philosophy

* Entropy and time
* Entropy and life
* Brownian ratchet
* Maxwell's demon
* Heat death paradox
* Loschmidt's paradox
* Synergetics

Theories

* Caloric theory

* Vis viva ("living force")
* Mechanical equivalent of heat
* Motive power

Key publications

* An Inquiry Concerning the
Source ... Friction

* On the Equilibrium of
Heterogeneous Substances

* Reflections on the
Motive Power of Fire

Timelines

* Thermodynamics
* Heat engines

* Art
* Education

* Maxwell's thermodynamic surface
* Entropy as energy dispersal

Scientists

* Bernoulli
* Boltzmann
* Bridgman
* Carathéodory
* Carnot
* Clapeyron
* Clausius
* de Donder
* Duhem
* Gibbs
* von Helmholtz
* Joule
* Kelvin
* Lewis
* Massieu
* Maxwell
* von Mayer
* Nernst
* Onsager
* Planck
* Rankine
* Smeaton
* Stahl
* Tait
* Thompson
* van der Waals
* Waterston

Other

* Nucleation
* Self-assembly
* Self-organization

* Category

* v
* t
* e

Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted.

In an equilibrium state the potentials, or driving forces, within the system, are in exact balance. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial state of thermodynamic equilibrium, subject to accurately specified constraints, to calculate, when the constraints are changed by an externally imposed intervention, what the state of the system will be once it has reached a new equilibrium. An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.

Equilibrium thermodynamics differs from non-equilibrium thermodynamics, in that, with the latter, the state of the system under investigation will typically not be uniform but will vary locally in those as energy, entropy, and temperature distributions as gradients are imposed by dissipative thermodynamic fluxes. In equilibrium thermodynamics, by contrast, the state of the system will be considered uniform throughout, defined macroscopically by such quantities as temperature, pressure, or volume. Systems are studied in terms of change from one equilibrium state to another; such a change is called a thermodynamic process.

Ruppeiner geometry is a type of information geometry used to study thermodynamics. It claims that thermodynamic systems can be represented by Riemannian geometry, and that statistical properties can be derived from the model. This geometrical model is based on the idea that there exist equilibrium states which can be represented by points on two-dimensional surface and the distance between these equilibrium states is related to the fluctuation between them.

## See also

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* Non-equilibrium thermodynamics
* Thermodynamics

## References

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* Adkins, C.J. (1983). Equilibrium Thermodynamics, 3rd Ed. Cambridge: Cambridge University Press.
* Cengel, Y. & Boles, M. (2002). Thermodynamics – an Engineering Approach, 4th Ed. (textbook). New York: McGraw Hill.
* Kondepudi, D. & Prigogine, I. (2004). Modern Thermodynamics – From Heat Engines to Dissipative Structures (textbook). New York: John Wiley & Sons.
* Perrot, P. (1998). A to Z of Thermodynamics (dictionary). New York: Oxford University Press.

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