Fundamental Relation for Gas of Interacting Particles in a Heat Flow

Hołyst, Robert; Makuch, Karol; Giżyński, Konrad; Maciołek, Anna; Żuk, Paweł J.

Fundamental Relation for Gas of Interacting Particles in a Heat Flow

Abstract

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, 𝑈(𝑆∗,𝑉,𝑁,𝑎∗,𝑏∗) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy 𝑆∗, volume V, number of particles N, and rescaled van der Waals parameters 𝑎∗, 𝑏∗. The state parameters, 𝑎∗, 𝑏∗, together with 𝑆∗, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Keywords

thermodynamics entropy steady-state excess heat nonequilibria

Citation

Hołyst, R.; Makuch, K.; Gi ˙zy ´nski, K.; Maciołek, A.; ˙Zuk, P.J. Fundamental Relation for Gas of Interacting Particles in a Heat Flow. Entropy 2023, 25, 1295. https:// doi.org/10.3390/e25091295

URI

https://open.icm.edu.pl/handle/123456789/25268

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