Free energy

In Thermodynamic free energy F (also called " free energy of Helmholtz") is a extensive function of state whose variation makes it possible to obtain the work useful likely to be provided by a thermodynamic Système closed, at constant temperature. It corresponds to the free energy of Helmholtz of the Anglo-Saxons, who prefer to symbolize it by the letter has .

Not to confuse with the function free Enthalpy G (" free energy of Gibbs " Anglo-Saxons), who applies to the systems evolving/moving at the temperature T and constant pressure (case of the reactions carried out with the free air).

The free energy is often used in the study of the explosions which induce a variation of pressure or in the Calorimétrie with constant volume carried out in a calorimetric Bombe.

Nevertheless the role of the function F is much less important in thermochemistry than that of the function free enthalpy which is the function headlight, essential to the study of the chemical balances.

Definition

Let us consider a irreversible transformation carried out at the temperature T and constant volume . If there is no electrochemical assembly, there is no electric work. Like V=cte , the work of the compressive forces is null.

Thus by applying the First principle: $\backslash \; Delta\; U\_\; \{syst\}\; =\; Q\_\; \{irrev\}\; ~$

Then let us apply the second principle: $\backslash \; Delta\; S\_\; \{creee\}\; =\; \backslash \; Delta\; S\_\; \{syst\}\; +\; \backslash \; Delta\; S\_\; \{ext.\}\; >\; 0~$

The system exchanges with the external medium Q_irrév . If one places side of the external medium, this one receives - Q (irrév) = - ΔU (syst) .

And the variation of entropy of the external medium becomes equal to:

$\backslash \; Delta\; S\_\; \{ext.\}\; =\; -\; \backslash \; frac\; \{Q\_\; \{irrev\}\}\; \{T\}\; =\; -\; \backslash \; frac\; \{\backslash \; Delta\; U\_\; \{syst\}\}\; \{T\}\; ~$

From where: $\backslash \; Delta\; S\_\; \{creee\}\; =\; \backslash \; Delta\; S\_\; \{syst\}\; -\; \backslash \; frac\; \{\backslash \; Delta\; U\_\; \{syst\}\}\; \{T\}\; >\; 0~$

Let us multiply by (- T)

One defines the function free energy thus:

For a transformation carried out with T and V = cte , one obtains:

If the transformation is reversible, $\backslash \; Delta\; S\_\; \{creee\}\; =\; 0~$ and $~\; (\backslash \; Delta\; F\_\; \{syst\})\; \_\; \{T,\; V\}\; =\; 0~$

On the other hand, if the transformation is irreversible, $\backslash \; Delta\; S\_\; \{creee\}\; >\; 0~$ and thus

Differential of F

$F\; =\; U\; -\; TS~$

$dF\; =\; of\; -\; TdS\; -\; the\; SdT~$

• Let us apply the First principle

$dU\; =\; \backslash \; delta\; Q\; +\; \backslash \; delta\; W\_\; \{FP\}\; +\; \backslash \; W\text{'}\; delta\; =\; \backslash \; delta\; Q\; -\; pdV\; +\; \backslash \; W\text{'}~$ delta

with:

δW_fp: work of the compressive forces

δW': different work, such as for example electric work in an assembly of pile

• Let us apply the second principle

$\backslash \; delta\; Q\_\; \{rev\}\; =\; TdS~$

thus expresses itself:
$dU\; =\; TdS\; -\; pdV\; +\; \backslash \; delta\; W\text{'}\; ~$

from where:

• If the temperature is constant:

$dF\; =\; -\; pdV\; +\; \backslash \; W\text{'}~$' delta

• Case of a real transformation thus Irreversible

One shows well that the variation of the function F is equal to the work provided by the system if the transformation is reversible and is carried out with T constant .

• If volume is constant and W' work is null:

more precisely:

The real transformation with T and V = cte, can be carried out only with one reduction in the free energy of the system. One can thus identify F with the Potentiel thermodynamics of a transformation Isotherme and Isochore

Useful relations starting from F or of its differentials

• Relation of Maxwell: $S=\; -\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; F\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_V$

• Relation of Gibbs-Helmholtz: there exists a relation similar to that of Gibbs-Helmholtz relating to F:

$\backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; \backslash \; left\; (\backslash \; frac\; \{F\}\; \{T\}\; \backslash \; right)\}\{\backslash \; partial\; T\}\; \backslash \; right)\; \_V\; =\; -\; \backslash \; frac\; \{U\}\; \{T^2\}$

• Potential chemical: a " définition" chemical potential can be given starting from a differential partial of F.

$\backslash \; mu\_i\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; F\}\; \{\backslash \; partial\; n\_i\}\; \backslash \; right)\; \_\; \{V,\; T,\; n\_\; \{J\; \backslash \; neq\; I\}\}$

Other functions of state

• Énergie interns

• free Enthalpie
• Enthalpie
• Entropie
• Température
• Volume
• Pression

Notice

The " term; energy libre" is employed as translation of free energy not when they are energy Helmholtz or Gibbs but in the case of the alleged supposed devices provided of energy without contribution any fuel, or with output higher than 1. These devices would violate the First principle of thermodynamics.

References

• IUPAC definition
• Atkins' Physical Chemistry , 7th edition, by Peter Atkins and Julio of Paula, Oxford University Close

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