Simple system Maxwell relations

The Maxwell relations (5.49a-d) are easy to rederive from the fundamental differential forms (5.46a-d). However, these relations are used so frequently that it is useful to employ a simple mnemonic device to recall their exact forms as needed. Sidebar 5.7 describes the thermodynamic magic square, which provides such a mnemonic for Maxwell relations and other fundamental relationships of simple (closed, single-component) systems. 

Conducting particles held in a nonconducting medium form a system which has a frequency-dependent dielectric constant. The dielectric loss in such a system depends upon the build-up of charges at the interfaces, and has been modeled for a simple system by Wagner [8], As the concentration of the conducting phase is increased, a point is reached where individual conducting areas contribute and this has been developed by Maxwell and Wagner in a two-layer capacitor model. Some success is claimed for the relation... 

We look at the simple gas laws to explore the behaviour of systems with no interactions, to understand the way macroscopic variables relate to microscopic, molecular properties. Finally, we introduce the statistical nature underlying much of the physical chemistry in this book when we look at the Maxwell-Boltzmann relationship. 

Thus, the Maxwell-Stefan diffusion coefficients satisfy simple symmetry relations. Onsager s reciprocal relations reduce the number of coefficients to be determined in a phenomenological approach. Satisfying all the inequalities in Eq. (6.12) leads to the dissipation function to be positive definite. For binary mixtures, the Maxwell-Stefan dififusivity has to be positive, but for multicomponent system, negative diffusivities are possible (for example, in electrolyte solutions). From Eq. (6.12), the Maxwell-Stefan diffusivities in an -component system satisfy the following inequality... 

The Maxwell-Stefan equations do not depend on choice of the reference velocity. For ideal gas mixtures, diffusivities Z) are independent of the composition, and equal to diffusivity D npf the hinary pair kl. In an w-component system, only n n-l)/2 different Maxwell-Stefan diffusivities are required as a result of the simple symmetry relations. Some advantages of the Maxwell-Stefan description of diffusion are ... 

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