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On a Carnot working continuum with non-equilibrium state parameters

100%

Ochrymiuk T. , Dudda W. , Badur J.

Archives of Thermodynamics

2023

tom Vol. 44, no 4

285--316

We explain that a full description of how the non-equilibrium state of the system evolves in time requires the consideration and solution of its general equation of motion. In the case of the Carnot medium, as a general equation of motion, there must be taken two balances of: nonequilibrium specific volume and non-equilibrium specific entropy. Instead of taking the classical approach where the balance of entropy is postponed to more advanced and theoretical treatments, we focus on the analysis of two, most general, volume and entropy fluxes. These fluxes of motion are universal features of thermodynamics. It has been shown that the Carnot working continuum mathematical model is captured by the two general nonmathematical statements valid for all systems that we call the first law and the second law of thermodynamics.

Thermodynamic Entropy from Sadi Carnot’s Cycle using Gauss’ and Doll’s-Tensor Molecular Dynamics

88%

Hoover W. G. , Hoover C. G.

Computational Methods in Science and Technology

2022

tom Vol. 28, No. 2

41--46

Carnot’s four-part ideal-gas cycle includes both isothermal and adiabatic expansions and compressions. Analyzing this cycle provides the fundamental basis for statistical thermodynamics. We explore the cycle here from a pedagogical view in order to promote understanding of the macroscopic thermodynamic entropy, the state function associated with thermal energy changes. From the alternative microscopic viewpoint the Hamiltonian H(q, p) is the energy and entropy is the (logarithm of the) phase-space volume Ω associated with a macroscopic state. We apply two novel forms of Hamiltonian mechanics to Carnot’s Cycle: (1) Gauss’ isokinetic mechanics for the isothermal segments and (2) Doll’s Tensor mechanics for the isentropic adiabatic segments. We explore the equivalence of the microscopic and macroscopic views of Carnot’s cycle for simple fluids here, beginning with the ideal Knudsen gas and extending the analysis to a prototypical simple fluid.