Hołyst R, Żuk PJ, Makuch K, Maciołek A, Giżyński K. Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow.
ENTROPY (BASEL, SWITZERLAND) 2023;
25:1483. [PMID:
37998175 PMCID:
PMC10670277 DOI:
10.3390/e25111483]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Revised: 10/23/2023] [Accepted: 10/24/2023] [Indexed: 11/25/2023]
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.
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