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{{Short description|Thermodynamic quantity}} |
{{Short description|Thermodynamic quantity}} |
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{{about|the mathematical concept used in thermodynamics|the engineering indicator|process variable}}{{Multiple issues|{{improve categories|date=November 2025}} |
{{about|the mathematical concept used in thermodynamics|the engineering indicator|process variable}} |
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{{Multiple issues|{{improve categories|date=November 2025}}{{single source|date=November 2025}}}} |
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{{Thermodynamics|cTopic=[[List of thermodynamic properties|System properties]]}} |
{{Thermodynamics|cTopic=[[List of thermodynamic properties|System properties]]}} |
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{{see also|List of thermodynamic properties}} |
{{see also|List of thermodynamic properties}} |
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In [[thermodynamics]], a [[quantity]] that is well defined so as to describe the path of a process through the [[equilibrium state]] space of a [[thermodynamic system]] is termed a ”’process function”’,<ref name=”Sychev1991″>{{cite book |last=Sychev |first=V. V. |title=The Differential Equations of Thermodynamics |year=1991 |publisher=Taylor & Francis |isbn=978-1560321217}}</ref> or, alternatively, a ”’process quantity”’, or a ”’path function”’. As an example, [[mechanical work]] and [[heat]] are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. |
In [[thermodynamics]], a [[quantity]] that is well defined so as to describe the path of a process through the [[equilibrium state]] space of a [[thermodynamic system]] is termed a ”’process function”’,<ref name=”Sychev1991″>{{cite book |last=Sychev |first=V. V. |title=The Differential Equations of Thermodynamics |year=1991 |publisher=Taylor & Francis |isbn=978-1560321217}}</ref> or, alternatively, a ”’process quantity”’, or a ”’path function”’. As an example, [[mechanical work]] and [[heat]] are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. |
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==Path functions== |
==Path functions== |
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Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include [[work (thermodynamics)|work]], [[heat]] and [[arc length]]. In contrast to path functions, [[state function]]s are independent of the path taken. Thermodynamic [[State function|state variables]] are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function. |
Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include [[work (thermodynamics)|work]], [[heat]] and [[arc length]]. In contrast to path functions, [[state function]]s are independent of the path taken. Thermodynamic [[State function|state variables]] are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function. |
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Latest revision as of 05:00, 2 December 2025
Thermodynamic quantity
In thermodynamics, a quantity that is well defined so as to describe the path of a process through the equilibrium state space of a thermodynamic system is termed a process function,[1] or, alternatively, a process quantity, or a path function. As an example, mechanical work and heat are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system.
Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include work, heat and arc length. In contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function.
Infinitesimal changes in a process function X are often indicated by δX to distinguish them from infinitesimal changes in a state function Y which is written dY. The quantity dY is an exact differential, while δX is not, it is an inexact differential. Infinitesimal changes in a process function may be integrated, but the integral between two states depends on the particular path taken between the two states, whereas the integral of a state function is simply the difference of the state functions at the two points, independent of the path taken.
Holonomic or non-holonomic
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In general, a process function X may be either holonomic or non-holonomic. For a holonomic process function, an auxiliary state function (or integrating factor) λ may be defined such that Y = λX is a state function. For a non-holonomic process function, no such function may be defined. In other words, for a holonomic process function, λ may be defined such that dY = λδX is an exact differential. For example, thermodynamic work is a holonomic process function since the integrating factor λ = 1/p (where p is pressure) will yield exact differential of the volume state function dV = δW/p. The second law of thermodynamics as stated by Carathéodory essentially amounts to the statement that heat is a holonomic process function since the integrating factor λ = 1/T (where T is temperature) will yield the exact differential of an entropy state function dS = δQ/T.[1]
- ^ a b Sychev, V. V. (1991). The Differential Equations of Thermodynamics. Taylor & Francis. ISBN 978-1560321217.
