Irreversible Thermodynamics and Coupling between Forces and Fluxes
The foundation of irreversible thermodynamics is the concept of entropy production
There is a natural and general coupling of the driving forces and corresponding fluxes that are present in a nonequilibrium system.
2.1 Entropy and Entropy Production
The conservation of internal energy is a consequence of the first law of thermodynamics.
The existence of the entropy state function is a consequence of the second law of thermodynamics.
In classical thermodynamics, the value of a system's entropy is not directly measurable but can be calculated.
In equilibrium thermodynamics, entropy maximization for a system with fixed internal energy determines equilibrium.
Consider a continuous system that demonstrates gradients in temperature, chemical potential, and other intensive thermodynamic quantities.
Fluxes of heat, mass, and other extensive quantities develop as the system approaches equilibrium.
Divide the system into small contiguous cells
The local equilibrium assumption is that the thermodynamic state of each cell is specified and in equilibrium with the local values of thermodynamic potentials.
Gibbs' fundamental relation can be used to calculate changes in the local equilibrium states as a result of evolution of the spatial distribution of thermodynamic potentials.
Divide dU through by a constant reference cell volume in order that all extensive quantities are on a per unit volume basis.
Equation 2.4 (derived by combining the first and second law) can be used to define the continuum limit for the change in entropy in terms of measurable quantities.
The differential terms are the first-order approximations to the increase of quantities at a point.
Because energy, heat, and mass may flow between cells during kinetic processes, they cannot be treated as isolated systems, and application of the second law must be generalized to the system of interacting cells.
It is useful to consider entropy as a fluxlike quantity capable of flowing from one part of a system to another, like energy, mass, and charge.
Entropy flux, denoted by Js, is related to heat flux.
Mass, charge, and energy are conserved quantities and additional restrictions on the flux of conserved quantities apply.
However, entropy is not conserved--it can be created or destroyed locally.
2.1.1 Entropy Production
The local rate of entropy-density creation is denoted by sigma dot.
Integrate to find the total rate of entropy creation in a volume.
In a general system, the total entropy increase depends upon how much entropy is produced within it and how much entropy flows through its boundaries.
The entropy flux is related to the sum of all potentials multiplying their conjugate fluxes.
Introduce the flux of heat.