Quasistatic process

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Note: Conjugate variables in italics

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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

Potentials

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

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Book:Thermodynamics

In thermodynamics, a quasi-static process is a thermodynamic process that happens slowly enough for the system to remain in internal equilibrium. An example of this is quasi-static compression, where the volume of a system changes at a rate slow enough to allow the pressure to remain uniform and constant throughout the system.^[1]

Any reversible process is necessarily a quasi-static one. However, some quasi-static processes are irreversible, if there is heat flowing (in to or out of the system) or if entropy is being created in some other way. An example of a quasi-static process that is not reversible is a compression against a system with a piston subject to friction — although the system is always in thermal equilibrium, the friction ensures the generation of dissipative entropy, which directly goes against the definition of reversible. A notable example of a process that is not even quasi-static is the slow heat exchange between two bodies at two finitely different temperatures, where the heat exchange rate is controlled by an approximately adiabatic partition between the two bodies — in this case, no matter how slowly the process takes place, the states of the two bodies are never infinitesimally close to equilibrium, since thermal equilibrium requires that the two bodies be at the same temperature.

Some ambiguity exists in the literature concerning the distinction between quasi-static and reversible processes, as these are sometimes taken as synonyms. The reason is the theorem that any reversible process is also a quasi-static one, even though (as we have illustrated above) the converse is not true. In practical situations, it is essential to differentiate between the two: any engineer would remember to include friction when calculating the dissipative entropy generation, so there are no reversible processes in practice. The definition given above is closer to the intuitive understanding of the word “quasi-” (almost) “static”, and remains technically different from reversible processes.

PV-Work in various quasi-static processes

Main articles: Work (thermodynamics) and Ideal gas equation

Constant pressure: Isobaric processes,
$W_{1-2}=\int PdV=P(V_{2}-V_{1})$
Constant volume: Isochoric processes,
$W_{1-2}=\int PdV=0$
Constant temperature: Isothermal processes,
$W_{1-2}=\int PdV,$ where P varies with V via $\quad PV=P_{1}V_{1}=C$ , so

$W_{1-2}=P_{1}V_{1}\ln {\frac {V_{2}}{V_{1}}}$
Polytropic processes,
$W_{1-2}={\frac {P_{1}V_{1}-P_{2}V_{2}}{n-1}}$

References

↑ Schroeder, Daniel (2000). An Introduction to Thermal Physics. United States: Addison Wesley Longman. pp. 20–21. ISBN 0-201-38027-7.

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Quasistatic process

PV-Work in various quasi-static processes

See also

References