Gibbs–Duhem equation

About: Gibbs–Duhem equation is a research topic. Over the lifetime, 393 publications have been published within this topic receiving 6248 citations. The topic is also known as: Gibbs-Duhem equation.

Information as a thermodynamic function of a living system

Abstract: It is suggested to introduce an information term into the Gibbs thermodynamic equation in the case of living systems. The possibility of describing the behavior of organisms by means of such an approach is shown.

Mass variables and chemical potentials in the Gibbs and De Donder formulations of chemical equilibrium

Abstract: The classical thermodynamic treatment of chemical equilibria in closed systems is founded on theoretical formulations by J.W. Gibbs and Th. De Donder. These two theories represent mathematically equivalent energy variation problems, related to each other through a mass variable transformation analogous to coordinate transformations in mechanics. Associated with the change in mass variables, chemical potentials of reactive substances are defined differently in the two theories, and are subject to different sets of constraints. Traditionally, the two sets of constraints have been merged into one, by assuming that the chemical potential represents the same variable in both theories, an assumption that is formally inconsistent with the difference in chemical potential definitions. Merging of constraints is still possible if chemical potentials remain invariant in value as a manifestation of symmetry under a Gibbs – De Donder mass transformation, but such symmetry has not been investigated. Here we demonstrate chemical potential invariance by reformulating De Donder’s theory using Lagrange multipliers, and combining the resulting constraints on chemical potentials with the classical Gibbs constraints, in a phase equilibration thought experiment. A new form of the Gibbs–Duhem (GD) relation is derived in the De Donder mass system. Comparing this relation to the classical GD equation in Gibbs’ component framework, subject to chemical potential invariance, directly yields the linear operator mapping the De Donder mass variables onto the set of Gibbs component masses. Results are illustrated for a simple ion exchange reaction, in the process solving the longstanding problem of determining solid exchanger activities in ion exchanging mixtures. It is pointed out that, even though the Gibbs and De Donder formulations are mathematically equivalent, the formal structure of De Donder’s theory allows a more explicit and systematic treatment of constraints, and also defines chemical masses in a form more naturally adapted to typical experimental measurements.

Interaction with thermal radiation in the free expansion and mixing of ideal gases and Gibbs' paradox in classical thermodynamics

Abstract: The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature of the theory since every material in this universe, and hence also the particles of a gas, absorbs and radiates thermal energy. The interaction with the thermal radiation that is contained within the volume of the body may be important in gases since the latter, unlike solids and liquids, are capable of undergoing conspicuous volume changes. Taking this interaction into account makes the behaviour of the ideal gases more realistic and removes Gibbs' paradox.