TITLE:
Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines
AUTHORS:
Hiroshi Uechi, Lisa Uechi, Schun T. Uechi
KEYWORDS:
Thermodynamic Consistency, Thermomechanical Dynamics (TMD), Nonlinear Differential Equation with Time-Dependent Coefficients, Nonequilibrium Irreversible States
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.6,
June
30,
2021
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, T(t)dS(t), , internal energy, dƐ(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.