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

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.10

SC.912.P.10.2

Maxwell's Thermodynamic Relations

Considere la forma diferencial de los potenciales termodinámicos; Las ecuaciones de Maxwell se pueden derivar de los potenciales termodinámicos.
La energía interna es una función de la entropía y el volumen. Dado que es un diferencial exacto, su derivada de segundo orden con respecto al volumen y la entropía no depende del orden de diferenciación.
Sustituyendo las expresiones de temperatura y presión se obtiene la primera relación de Maxwell.
La entalpía depende de la entropía y la presión. Tomando la derivada de segundo orden y sustituyendo las expresiones de temperatura y volumen se obtiene la segunda relación de Maxwell.
La energía libre de Helmholtz depende del volumen y la temperatura. Expresándola como una derivada de segundo orden y sustituyendo las expresiones de presión y entropía da la tercera relación de Maxwell.
La energía libre de Gibbs es una función de la presión y la temperatura. Diferenciándola dos veces y sustituyendo las relaciones de volumen y entropía se obtiene la cuarta relación de Maxwell.
Las ecuaciones de Maxwell se utilizan para resolver problemas termodinámicos complejos, ya que relacionan un diferencial parcial entre cantidades que son difíciles de medir experimentalmente con un diferencial parcial entre cantidades fácilmente medibles.

<ol>
	<li>Blundell, S.J. y Blundell, K.M. (2010). Conceptos de Física Térmica. Segunda Edición. Nueva York, Estados Unidos: Oxford University Press. pp. 179.</li>
	<li>Helrich, C.S. (2009). Termodinámica Moderna con Mecánica Estadística. Segunda Edición. Berlín: Springer. Págs. 69.</li>
</ol>

relaciones termodinámicas de maxwell

Las relaciones termodinámicas de Maxwell son muy útiles para resolver problemas en termodinámica. Cada una de las relaciones de Maxwell relaciona una derivada parcial entre magnitudes que pueden ser difíciles de medir experimentalmente con una derivada parcial entre magnitudes que pueden ser fácilmente medidas. Estas relaciones son un conjunto de ecuaciones que se derivan de la simetría de las segundas derivadas y de los potenciales termodinámicos. Todos los potenciales termodinámicos son diferenciales exactos. Por lo tanto, su segunda derivada no depende del orden de diferenciación. En el caso de las relaciones de Maxwell, el potencial termodinámico se expresa en términos de las derivadas parciales de esa función. Sustituyendo los valores de las derivadas parciales se obtienen las ecuaciones de Maxwell. Las cuatro relaciones de Maxwell son: <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;"> Estas ecuaciones relacionan cambios en la entropía, que son difíciles de medir, con cambios en otras variables termodinámicas, como temperatura, volumen y presión, que son más fáciles de medir. Por ejemplo, en la última ecuación, el término del lado izquierdo da el cambio en la presión con la temperatura a volumen constante. Esta magnitud se puede medir fácilmente en un laboratorio. Sin embargo, el término del lado derecho de la ecuación es más complicado, ya que es difícil medir el cambio de entropía con el volumen a temperatura constante.

Relaciones termodinámicas de Maxwell

Las relaciones termodinámicas de Maxwell son muy útiles para resolver problemas de termodinámica. Cada una de las relaciones de Maxwell relata una ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

The First Law of Thermodynamics

La primera ley de la termodinámica

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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Open, Closed, and Isolated Systems

A thermodynamic system is the part of the world that scientists study for its heat and energy behavior. It sits inside a surrounding environment, or surroundings. The system and the surroundings can exchange heat and do work across the boundary that separates them. The immediate surroundings affect the system most strongly because they interact with it directly. A kettle of boiling tea shows how this works in everyday life. The tea and the kettle together form the system. If the lid is open,...

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Constant Volume and Pressure in Thermodynamics

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Ideal gas heat capacity depends on degrees of freedom, which are the independent ways a gas molecule can move, rotate, and vibrate. If d is the number of degrees of freedom, the molar heat capacity at constant volume can be written in terms of d. The molar heat capacity at constant pressure can also be written using the relationship between the two heat capacities. The ratio of molar heat capacity at constant pressure to molar heat capacity at constant volume is called the ratio of heat...

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Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

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Adiabatic Compression in an Engine Cylinder

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Energy Forms in Thermodynamics

Thermodynamic potentials are energy-based state functions used to analyze a thermodynamic system. They help describe how a system changes under different conditions. The four main thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These potentials can be written using two of the variables pressure, volume, temperature, and entropy. In each case, the rate of change of the potential with respect to the other two variables gives useful...

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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.

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Gas cooling and heating in throttling is explained by the Joule-Thomson effect, also called the Joule-Kelvin effect. It describes how a fluid changes temperature when it passes through a valve or porous plug in a thermally insulated system. This type of flow is called a throttling process. In the experiment, a high-pressure gas is forced through a throttle valve or porous plug into a lower-pressure region. The gas expands as it moves into the larger volume. Work is done on the gas as it is...

key terms and concepts

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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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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