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Changing short description from "mathematical function that considers only the start and end states of the system it describes" to "Function describing equilibrium states of a system" |
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In the [[Thermodynamics#Equilibrium thermodynamics|thermodynamics of equilibrium]], a '''state function''', '''function of state''', or '''point function''' for a [[thermodynamic system]] is a [[Function (mathematics)|mathematical function]] relating several [[state variables]] or state quantities (that describe [[Thermodynamic equilibrium|equilibrium states]] of a system) that depend only on the current equilibrium [[thermodynamic state]] of the system<ref>{{harvnb|Callen|1985|pages=5,37}}</ref> (e.g. gas, liquid, solid, crystal, or [[emulsion]]), not the [[Thermodynamic process path|path]] which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The [[ideal gas law]] is a good example. In this law, one state variable (e.g., pressure, volume, temperature, or the amount of substance in a gaseous equilibrium system) is a function of other state variables so is regarded as a state function. A state function could also describe the number of a certain type of atoms or molecules in a gaseous, liquid, or solid form in a [[Heterogeneous mixture|heterogeneous]] or [[homogeneous mixture]], or the amount of energy required to create such a system or change the system into a different equilibrium state.
[[Internal energy]], [[enthalpy]], and [[entropy]] are examples of state quantities or state functions because they quantitatively describe an equilibrium state of a [[thermodynamic system]], regardless of how the system has arrived in that state. They are expressed by [[exact differential]]s. In contrast, [[mechanical work]] and [[heat]] are [[process quantities]] or path functions because their values depend on a specific "transition" (or "path") between two equilibrium states that a system has taken to reach the final equilibrium state, being expressed by [[inexact differential]]s.
==History==
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In the equation,
The notation {{mvar|d}} will be used for an exact differential. In other words, the integral of {{math|''d''Φ}} will be equal to {{math|Φ(''t''<sub>1</sub>) − Φ(''t''<sub>0</sub>)}}. The symbol {{mvar|δ}} will be reserved for an [[inexact differential]], which cannot be integrated without full knowledge of the path. For example, {{math|1=''δW'' = ''PdV''}} will be used to denote an infinitesimal increment of work.
State functions represent quantities or properties of a thermodynamic system, while non-state functions represent a process during which the state functions change. For example, the state function {{math|''PV''}} is proportional to the [[internal energy]] of an ideal gas, but the work {{mvar|W}} is the amount of energy transferred as the system performs work. Internal energy is identifiable; it is a particular form of energy. Work is the amount of energy that has changed its form or ___location.
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