Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

Abstract

The irreversible mechanism of heat engines is studied in terms of thermodynamic consistency and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The couplings among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, ( ) ( ) d T t t  , internal energy, ( ) d t  , and thermodynamic work, ( )dW t , are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.

Deconfinement of nonstrange hadronic matter with nucleons and Δ baryons to quark matter in neutron stars

“…1,5 Of the various models considered in literature to explain the properties of pure quark matter and mixed phases, in the present work, we consider a simple form of MIT bag model 89 with corrections due to strong repulsive interactions in the thermodynamic quark potential 56,[90][91][92][93] to describe unpaired quark phase. First order correction due to strong interaction 92 and perturbative effects 62,[93][94][95][96][97] may also be considered but several works 27,[98][99][100][101][102] emphasize that the effects of perturbative corrections can also be realized by changing the bag constant. The mixed phase properties like critical density for appearance of quarks, the density range over which mixed phase can extend and the EoS etc.…”

The Application of Thermomechanical Dynamics (TMD) to the Analysis of Nonequilibrium Irreversible Motion and a Low-Temperature Stirling Engine

“…Therefore, the nonlinear differential equations with constant and time-dependent parameters must be mathematically categorized respectively as a different class of nonlinear equations. This is one of the important mathematical properties discovered in the TMD analysis of a drinking bird system [1].…”

“…In the current paper, we apply the TMD model to a low-temperature Stirling engine [5] in order to study thermomechanical motion and time-progressing internal thermodynamic quantities. The three propositions in the TMD method are [1]:…”

“…It is important to understand that the mechanism of energy conversion goes through a nonequilibrium irreversible state, and so, it is necessary to have a theoretical model or method to study nonequilibrium irreversible states. The Thermomechanical Dynamics (TMD) is a theoretical model proposed for the first time by the authors of this paper to study Nonequilibrium Irreversible States (NISs), which is constructed from the TMD analysis of a drinking bird [1] [2]. The drinking bird's equation of motion, the dissipative equation of motion, is consistently solved, producing time-evolving thermodynamic quantities, such as internal energy, work, entropy, and temperature.…”

A Detailed Analysis of the Special Points on $M-R$ Solutions of Hybrid (Twin) Stars

“…In the present work, we consider the simplistic form of the Bag model without involving the strong repulsive interactions between the quarks. First order correction due to strong interaction [92] and perturbative effects [10,[93][94][95][96] may also be considered. However, [8,19,[35][36][37][38][39][40] noted that the effects of perturbative corrections can also be realized by varying the bag pressure.…”