Volume 35, Issue 2

A simplified dynamical system is developed in this paper for unsteady regimes of standing-wave thermoacoustic engines. A lumped thermal capacity model is applied for thermal analysis, including thermoacoustically induced heat transfer. At a critical value of a temperature gradient in the engine stack, the fundamental acoustic mode is excited in the engine resonator. Simulation results demonstrate a possibility of different start-up processes in the engine brought in contact with a high-temperature source. High-amplitude acoustic bursts coupled with thermal cycles may appear initially; and a stable limit-cycle regime is established after several cycles. With sufficiently large nonlinear losses present in the system, a monotonic increase of acoustic oscillations is demonstrated. Similar results have been observed in experiments.

Conventional linear thermodynamic description of chemical mass transport is based on Onsager equations for flows proportional to thermodynamic forces, and analysis of expressions for entropy production. A recently developed mesoscopic thermodynamic description is able to explain also nonlinear chemical kinetics phenomena. An alternative unifying approach is summarized here and is essentially an extension of classical mechanics. It is based on the idea that the mass transfer flow is the product of Einstein's mobility, concentration, and a gradient of physicochemical potential, which is a more general than usual chemical potential. The approach easily leads to many classical equations for mass transport, including Fick's law and the Fokker–Einstein expression for diffusion coefficient, Smoluchowski and Fokker–Planck equations for simultaneous diffusion and force-driven transport, and Boltzmann distribution. Addition of a chemical reaction coordinate naturally leads to a general description of kinetics of elementary chemical reactions far fromequilibrium, which includes dimensions and dielectric properties of molecules but does not need reorganization energy. It easily leads to Arrhenius, transition state theory, and Kramers equations for the rate of elementary chemical reaction, Gibbs and Nernst equations for chemical and electrochemical equilibrium, Butler–Volmer and Tafel equations for kinetics of electrochemical reactions, the Schottky equation for semiconductor diodes, more general than Guldberg–Waage law for equilibrium, and so on. A new interpretation of classic Einstein's mobility in quantum mechanics terms is suggested. Using this approach it is possible to explain the effects of all possible driving factors on chemical reactions and even to give a general description of chemical kinetics, which uses physicochemical potential and does not include concentrations or activities.

A numerical model of a hard-sphere fluid on either side of a compound piston shows that damping occurs naturally without invoking extraneous mechanisms such as friction. Inter-particle collisions are identified as being responsible. Whereas only the component of particle momentum in the direction of the piston motion is affected by the collisions with the piston, inter-particle collisions affect the other components of momentum and effectively dissipate the energy of the piston. These ideas are then incorporated into a simpler, one-dimensional numerical model based on kinetic theory in which all the particles have the same initial energy and inter-particle collisions are simulated by randomly adjusting the energy distribution. Varying the rate of energy redistribution alters the rate of decay of the piston motion, but we find the net work done to be dependent only on the starting conditions and quite independent of the detailed motion. This allows the consequences for thermodynamics of this intrinsic dissipation process to be investigated. We find that the adiabatic compound piston is irreversible, with the net work done being given by the product of the final pressure and the volume change. This finding is supported mathematically and we propose a simple method for determining the final piston position.

Energy plays only a minor role in orthodox theories of economic growth, because standard economic equilibrium conditions say that the output elasticity of a production factor, which measures the factor's productive power, is equal to the factor's share in total factor cost. Having commanded only a tiny cost share of about 5 percent so far, energy is often neglected altogether. On the other hand, energy conversion in the machines of the capital stock has been the basis of industrial growth. How can the physically obvious economic importance of energy be reconciled with the conditions for economic equilibrium, which result from the maximization of profit or overall welfare? We show that these equilibrium conditions no longer yield the equality of cost shares and output elasticities, if the optimization calculus takes technological constraints on the combinations of capital, labor, and energy into account. New econometric analyses of economic growth in Germany, Japan, and the USA yield output elasticities that are for energy much larger and for labor much smaller than their cost shares. Social consequences are discussed.

A model of suspensions of deformable polymeric chains in dilute solutions is proposed. The originality of the model lies in raising the relative motion of polymers with respect to the solvent to the status of independent variables, at the same level of such classical variables as global mass, mass fraction, temperature, and conformation tensor. Such an attitude is typical of extended irreversible thermodynamics. It is shown that the restrictions placed by the second law of thermodynamics leads to the various expressions of the constitutive and evolution equations governing the model. The use of Onsager's reciprocal relations and the criterion of frame indifference is also commented upon.