Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow

Author:

Hołyst Robert1ORCID,Żuk Paweł12ORCID,Makuch Karol1ORCID,Maciołek Anna13ORCID,Giżyński Konrad1ORCID

Affiliation:

1. Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland

2. Department of Physics, Lancaster University, Lancaster LA1 4YB, UK

3. Max-Planck-Institut für Intelligente Systeme Stuttgart, Heisenbergstr. 3, D-70569 Stuttgart, Germany

Abstract

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that the total internal energy U(S*,V,N,L,M*) is the function of the following parameters of state: the non-equilibrium entropy S*, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle M*. Each parameter corresponds to a different way of energy exchange with the environment. The parameter M* changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy S* and effective mass M*. When the heat flow goes to zero, S* approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium.

Funder

European Union

Minister of Science and Higher Education

Publisher

MDPI AG

Subject

General Physics and Astronomy

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