On Thermodynamics Problems in the Single-Phase-Lagging Heat Conduction Model

Shu-Nan Li,Bing-Yang Cao

doi:10.3390/e18110391

Abstract

Thermodynamics problems for the single-phase-lagging (SPL) model have not been much studied. In this paper, the violation of the second law of thermodynamics by the SPL model is studied from two perspectives, which are the negative entropy production rate and breaking equilibrium spontaneously. The methods for the SPL model to avoid the negative entropy production rate are proposed, which are extended irreversible thermodynamics and the thermal relaxation time. Modifying the entropy production rate positive or zero is not enough to avoid the violation of the second law of thermodynamics for the SPL model, because the SPL model could cause breaking equilibrium spontaneously in some special circumstances. As comparison, it is shown that Fourier’s law and the CV model cannot break equilibrium spontaneously by analyzing mathematical energy integral.

Highlights

Fourier’s law of heat conduction, which shows the connection between temperature gradient and heat flux, is often used to describe normal heat conduction problems: q + λ∇ T = 0, (1)where q is the heat flux, λ is the thermal conductivity and T is the temperature
Modifying the entropy production rate to a positive or zero value is not enough to avoid the violation of the second law of thermodynamics for the SPL model, because the SPL model could cause spontaneous equilibrium breaking in some special circumstances
For the SPL model, modifying the entropy production rate is not enough to avoid the violation of the second law of thermodynamics

Summary

Introduction

Fourier’s law of heat conduction, which shows the connection between temperature gradient and heat flux, is often used to describe normal heat conduction problems:. The violation of the second law of thermodynamics by the SPL model is studied from two perspectives, which are the negative entropy production rate and the spontaneous breaking of equilibrium. Compared with the CV model, the methods for the SPL model to avoid the negative entropy production rate are proposed from two perspectives, which are extended irreversible thermodynamics and the thermal relaxation time. Modifying the entropy production rate to a positive or zero value is not enough to avoid the violation of the second law of thermodynamics for the SPL model, because the SPL model could cause spontaneous equilibrium breaking in some special circumstances. It is shown why Fourier’s law and the CV model cannot break equilibrium spontaneously by analyzing the mathematical energy integral

Entropy Production Rate

Thermal Relaxation Time

Spontaneous Equilibrium

Mathematical Energy Integral

Conclusions