Name: using maxwell's relations in thermodynamics
Uploaded: 2025-05-22T09:05:59.000Z
Duration: 1 min 23 s
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K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.10

SC.912.P.10.2

Maxwell's Thermodynamic Relations

Considérons la forme différentielle des potentiels thermodynamiques ; Les équations de Maxwell peuvent être dérivées des potentiels thermodynamiques.
L’énergie interne est fonction de l’entropie et du volume. Comme il s’agit d’une différentielle exacte, sa dérivée du second ordre par rapport au volume et à l’entropie ne dépend pas de l’ordre de dérivation.
En substituant les expressions de température et de pression, on obtient la première relation de Maxwell.
L’enthalpie dépend de l’entropie et de la pression. En prenant la dérivée du second ordre et en substituant les expressions de la température et du volume, on obtient la deuxième relation de Maxwell.
L’énergie libre de Helmholtz dépend du volume et de la température. L'exprimer comme une dérivée du second ordre et y substituer les expressions de pression et d'entropie donne à la troisième la relation de Maxwell.
L’énergie libre de Gibbs est fonction de la pression et de la température. En la dérivant deux fois et en substituant les relations de volume et d'entropie, on obtient la relation de Maxwell au quatrième.
Les équations de Maxwell sont utilisées pour résoudre des problèmes thermodynamiques complexes car elles associent une différentielle partielle entre des quantités difficiles à mesurer expérimentalement à une différentielle partielle entre des quantités facilement mesurables.

<ol>
	<li>Blundell, S.J. et Blundell, K.M. (2010). Concepts en physique thermique. Deuxième édition. New York, États-Unis : Oxford University Press. p. 179.</li>
	<li>Helrich, C.S. (2009). Thermodynamique moderne avec mécanique statistique. Deuxième édition. Berlin : Springer. p. 69.</li>
</ol>

les relations thermodynamiques de maxwell

Les relations thermodynamiques de Maxwell sont très utiles pour résoudre des problèmes en thermodynamique. Chacune des relations de Maxwell relie une dérivée partielle entre des quantités qui peuvent être difficiles à mesurer expérimentalement à une dérivée partielle entre des quantités qui peuvent être facilement mesurées. Ces relations sont un ensemble d'équations dérivables de la symétrie des secondes dérivées et des potentiels thermodynamiques.

Tous les potentiels thermodynamiques sont des différentielles exactes. Par conséquent, leur dérivée d'ordre deux ne dépend pas de l'ordre de la différenciation. Dans le cas des relations de Maxwell, le potentiel thermodynamique est exprimé en termes des dérivées partielles de cette fonction. En substituant les valeurs des dérivées partielles, on obtient les équations de Maxwell. Les quatre relations de Maxwell sont :

<img alt="Equation1" src="/files/ftp_upload/14173/14173_Equation_1.png" style="text-align: center; height: 32px;" />

<img alt="Equation2" src="/files/ftp_upload/14173/14173_Equation_2.png" style="text-align: center; height: 35px;" />

<img alt="Equation3" src="/files/ftp_upload/14173/14173_Equation_3.png" style="text-align: center; height: 34px;" />

<img alt="Equation4" src="/files/ftp_upload/14173/14173_Equation_4.png" style="text-align: center; height: 35px;" />

Ces équations relient les variations d'entropie, qui sont difficiles à mesurer, avec les variations d'autres variables thermodynamiques, comme la température, le volume et la pression, qui sont plus faciles à mesurer. Par exemple, dans la dernière équation, le terme du côté gauche donne la variation de pression avec la température à volume constant. Cette quantité peut être facilement mesurée en laboratoire. Cependant, le terme du côté droit de l'équation est plus compliqué, car il est difficile de mesurer la variation d'entropie avec le volume à température constante.

Les relations thermodynamiques de Maxwell

Les relations thermodynamiques de Maxwell sont très utiles pour résoudre des problèmes en thermodynamique. Chacune des relations de Maxwell relate une ...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

The First Law of Thermodynamics

Le premier principe de la thermodynamique

KEY TERMS AND CONCEPTS

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using maxwell's relations in thermodynamics

Maxwell's thermodynamic relations help solve problems in thermodynamics. They connect partial differentials for quantities that are hard to measure in the lab with quantities that are easier to measure. This makes them useful for working with temperature, pressure, volume, and entropy.

These relations come from thermodynamic potentials and the symmetry of second derivatives. Thermodynamic potentials are exact differentials, so the order of second differentiation does not change the result. When the partial derivatives of these functions are substituted, Maxwell's equations are obtained.

There are four Maxwell's relations. Together, they link changes in entropy, which are difficult to measure, to changes in other thermodynamic variables that are easier to observe. For example, one relation gives the change in pressure with temperature at constant volume. That term can be measured in the laboratory. The matching entropy term with volume at constant temperature is harder to measure directly.

Using Maxwell's Relations in Thermodynamics

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Learn how Maxwell's thermodynamic relations connect hard-to-measure entropy changes with measurable temperature, pressure, and volume relationships.

Using Maxwell's Relations in Thermodynamics | JoVE K12

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SC.912.P.10.6

A. Energy is involved in all physical and chemical processes. It is conserved, and can be transformed from one form to another and into work. At the atomic and nuclear levels energy is not continuous but exists in discrete amounts. Energy and mass are related through Einstein's equation E=mc2.

B. The properties of atomic nuclei are responsible for energy-related phenomena such as radioactivity, fission and fusion.

C. Changes in entropy and energy that accompany chemical reactions influence reaction paths. Chemical reactions result in the release or absorption of energy.

D. The theory of electromagnetism explains that electricity and magnetism are closely related. Electric charges are the source of electric fields. Moving charges generate magnetic fields.

E. Waves are the propagation of a disturbance. They transport energy and momentum but do not transport matter.

Using Maxwell's Relations in Thermodynamics

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