# 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 propertiesNote: 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 
$c=$
$T$$\partial S$$N$$\partial T$
Compressibility 
$\beta =-$
$1$$\partial V$$V$$\partial p$
Thermal expansion 
$\alpha =$
$1$$\partial V$$V$$\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 $U(S,V)$Enthalpy $H(S,p)=U+pV$Helmholtz free energy $A(T,V)=U-TS$Gibbs free energy $G(T,p)=H-TS$ :
HistoryCulture
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
ArtEducation
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
Order and disorder :
Category :
vte :
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.