Equilibrium thermodynamics

Thermodynamics
The classical Carnot heat engine
Branches Classical Statistical Chemical Quantum thermodynamics Equilibrium / Non-equilibrium
Laws Zeroth First Second Third
Systems State Equation of state Ideal gas Real gas State of 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  [math]\displaystyle{ c= }[/math] [math]\displaystyle{ T }[/math] [math]\displaystyle{ \partial S }[/math] [math]\displaystyle{ N }[/math] [math]\displaystyle{ \partial T }[/math] Compressibility  [math]\displaystyle{ \beta=- }[/math] [math]\displaystyle{ 1 }[/math] [math]\displaystyle{ \partial V }[/math] [math]\displaystyle{ V }[/math] [math]\displaystyle{ \partial p }[/math] Thermal expansion  [math]\displaystyle{ \alpha= }[/math] [math]\displaystyle{ 1 }[/math] [math]\displaystyle{ \partial V }[/math] [math]\displaystyle{ V }[/math] [math]\displaystyle{ \partial T }[/math]
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 [math]\displaystyle{ U(S,V) }[/math] Enthalpy [math]\displaystyle{ H(S,p)=U+pV }[/math] Helmholtz free energy [math]\displaystyle{ A(T,V)=U-TS }[/math] Gibbs free energy [math]\displaystyle{ G(T,p)=H-TS }[/math]
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 Theory of heat Vis viva ("living force") Mechanical equivalent of heat Motive power Key publications "An Experimental Enquiry Concerning ... Heat" "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 Carnot Clapeyron Clausius Carathéodory Duhem Gibbs von Helmholtz Joule Maxwell von Mayer Onsager Rankine Smeaton Stahl Thompson Thomson van der Waals Waterston
Book Category
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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

• Non-equilibrium thermodynamics
• Thermodynamics

References

• 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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