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Process function

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Thermodynamic quantity

This article is about the mathematical concept used in thermodynamics. For the engineering indicator, seeprocess variable.

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Thermodynamics

The classicalCarnot heat engine

Branches

Equilibrium / Non-equilibrium

Laws

Systems

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 initalics

Process functions
Property diagrams Intensive and extensive properties
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=

$T {\displaystyle T}$	$\partial S$
$N {\displaystyle N}$	$\partial T$

Compressibility

\beta =-

$1 {\displaystyle 1}$	$\partial V$
$V {\displaystyle V}$	$\partial p$

Thermal expansion

\alpha =

$1 {\displaystyle 1}$	$\partial V$
$V {\displaystyle V}$	$\partial T$

Equations

Potentials

Internal energy
$U(S,V)$
Enthalpy
$H(S,p)=U+pV$
Helmholtz free energy
$A(T,V)=U-TS$
Gibbs free energy
$G(T,p)=H-TS$

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

Other

Category

Inthermodynamics, aquantity that is well defined so as to describe the path of a process through theequilibrium state space of athermodynamic system is termed aprocess function,^[1] or, alternatively, aprocess quantity, or apath function. As an example,mechanical work andheat are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system.

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 includework,heat andarc length. In contrast to path functions,state functions are independent of the path taken. Thermodynamicstate 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.

Differentials

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Infinitesimal changes in a process functionX are often indicated byδX to distinguish them from infinitesimal changes in a state functionY which is writtendY. The quantitydY is anexact differential, whileδX is not, it is aninexact 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 functionX may be eitherholonomic or non-holonomic. For a holonomic process function, an auxiliary state function (or integrating factor)λ may be defined such thatY =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 thatdY =λδX is an exact differential. For example, thermodynamic work is a holonomic process function since the integrating factorλ =⁠1/p⁠ (wherep is pressure) will yield exact differential of the volume state functiondV =⁠δW/p⁠. Thesecond law of thermodynamics as stated byCarathéodory essentially amounts to the statement that heat is a holonomic process function since the integrating factorλ =⁠1/T⁠ (whereT is temperature) will yield the exact differential of an entropy state functiondS =⁠δQ/T⁠.^[1]