Signe Kjelstrup

The Role of the Transported Entropy of Lead Ions in Partially Thermostated and Adiabatic Cells

electrolyte bulk phase. The phases between the bulk phases are twodimensional Gibbs interfaces ~or surfaces!. These phases are the two surfaces between the molybdenum and the lead metals and the two electrode surfaces between the bulk electrode and bulk electrolyte. The surfaces may, in principle, have ~four! different temperatures. A chemical potential gradient develops due to the temperature gradient across the electrolyte ~typically in a few hours!, and we examine the stationary state when the gradient is being balanced by the thermal force. The currentless potential of the system is used to derive the transported entropies in the system. The aim of the work is to use these quantities in a more general discussion of the electric potential profile of the cell. The concentration distribution is time independent in the stationary state. One advantage with the present system is also that the stationary state can be achieved in a relatively short time, 11,12 that is, 2-3 h. The moles of PbCl2 transferred across the cell per faraday passing in the outer circuit is therefore zero, J PbCl2 5 0. It also follows, that the flux of MCl is zero. Lead ions formed at the left electrode, carry the net charge across the electrolyte, and react to form metal at the right hand side electrode. The overall chemical reaction of cell a is

Chapter 12:Electrochemical Energy Conversion

We show how non-equilibrium thermodynamics can be used to describe energy conversion in electrochemical cells. The entropy production is actively used to find the electric potential profile under reversible conditions and to define the overpotential. Two variable sets are useful, and we give the transformations between these. We next prescribe procedures for calculations of profiles of temperature, concentrations and electric potential across a cell. Applications to saline power plants and thermoelectric generators are briefly discussed.

Chapter 13:Entropy Production Minimization with Optimal Control Theory

This chapter discusses how to take advantage of optimal control theory to minimize the entropy production of process units, in a step-wise, practical approach. The main results from literature are discussed, e.g. the validity of the theorems of equipartition of entropy production or equipartition of forces, as approximations to the state of minimum entropy production. A common property of systems with possibilities for internal equilibration seems to be that operating paths with minimum entropy production constitute bands in state space, called highways in state space. We show how energy-efficient design can be facilitated with knowledge of these properties.

Chapter 1:Basis and Scope

This book is a collection of chapters which report on recent developments in the field of non-equilibrium thermodynamics. It is meant for readers that would like to know what the field can add to their understanding of transport phenomena, or what it means for experimental design. Classical non-equilibrium thermodynamics was established in 1931 and developed during the subsequent thirty years for transport in homogeneous phases. This chapter gives a short presentation of the basic assumptions, along with advice on how to derive the entropy production and find the flux–force relations for transport of heat, mass and charge. In the end of the chapter, we put the subsequent chapters of the book into perspective. The book presents recent results for homogeneous systems, for mesoscopic systems and for heterogeneous systems.

Chapter 4:Local Equilibrium in Non-equilibrium Thermodynamics

The hypothesis of local equilibrium is central in non-equilibrium thermodynamics. We define and review support for this hypothesis for three-, two- and one-dimensional, macroscopic thermodynamic systems. The hypothesis can also be supported in mesoscopic systems. It does not apply to density-gradient theories as these introduce nonlocal variables, but is found to apply if we define surface excess variables according to Gibbs. The hypothesis can therefore be actively used to predict surface properties.

Chapter 8:Non-equilibrium Thermodynamics for Evaporation and Condensation

Non-equilibrium thermodynamics gives dynamic boundary conditions for transport of heat and mass into and through surfaces far from reversible conditions. Conversions between thermal, mechanical and chemical energy are described through force–flux relations. Among the transfer coefficients, the coupling coefficient is large at interfaces, unlike in the homogeneous phase. The magnitude and sign of the coupling coefficient are determined by the enthalpy of the phase transformation. This has a bearing on the modelling of phase transitions, as simple laws of transport become insufficient, even wrong. The coefficients for evaporation and condensation are given and compared to results from kinetic theory. Transfer coefficients from experiments, molecular dynamics simulations and from the use of the van der Waals square gradient theory, are reviewed. The need for more work along these lines is pointed out. A short discussion is also given about contact lines.

Chapter 14:Applied Non-Equilibrium Thermodynamics

Non-equilibrium thermodynamics describes all kinds of transport processes. This chapter must focus on a few, namely transport of heat and mass in homogeneous and heterogeneous systems, in the absence or presence of chemical reactions. This introduction gives a brief history of the field, a list of g...