Volume 24, Issue 3

Constitutive relations are derived for the evolution of specific volume and specific enthalpy in amorphous glassy polymers after thermal treatment. The Robertson approach is extended to infinite ensembles of cells, and a nonlinear partial differential equation is developed for the probability density of free volume. This equation is resolved explicitly under plausible assumptions, whose validity is verified by comparison with observations for polystyrene. As a result, two ordinary differential equations are obtained for the excess specific volume and the excess specific enthalpy, which provide a molecular basis for the Kovacs phenomenological relations. It is demonstrated that in one-step thermal tests, the rate of change in the specific enthalpy exceeds by twice that for the specific volume. This conclusion is confirmed by experimental data for polycarbonate and polystyrene.

We have measured with the thermogravitational method the Soret coefficient of the binary liquid systems: benzene+nhexane, toluene+nheptane and carbon tetrachloride with heptane and hexane, in a well characterized column used in a previous work to measure the systems benzene+nheptane and toluene+nhexane. The obtained results show that the Soret coefficient takes nearly the same value in the mixtures of each one of the components, benzene, toluene or carbon tetrachloride with hexane and heptane. For all the systems considered it varies slowly with the concentration and is nearly independent of temperature. The higher values of the thermal diffusion factor correspond to mixtures containing carbon tetrachloride. Previous results for these systems were obtained in an imperfect apparatus and must be disregarded.

Consideration is given to a microscale structure consisting of a thin porous medium filled with interstitial Ouid or a microscale regime with binary species of atoms. An example is a cellular membrane. This paper treats a one-dimensional model consisting of atoms of heavier mass M alternating with atoms of lighter mass m arranged in a series. Like photons, elastic vibrations of atoms or phonons propagate as waves. The problem of phonon transport, referring to heat conduction in the microscale regime, is formulated in terms of the displacements of atoms from their equilibrium positions. With the displacements treated as a wave motion, the frequency-wave number relationship for the heterogeneous-atomic membrane is obtained. Two modes of wave transport are obtained and their roles in phonon transport are discussed.

We examine the problem of energy-efficient production in an industrial process. By energy-efficient we mean minimum entropy production. We use the possibility to redistribute the production in different times or parts of the system for a given total production, and show that a distribution, that equipartitions the derivative of the local entropy production rate with respect to the local production, minimizes the entropy production. Equipartition in time implies stationary state production. Equipartition in space implies production for a given position independent force. The same constant derivative of the local entropy production rate is found if ones optimizes the production for a given total entropy production. Close of equilibrium the equipartition condition is found to reduce to the isoforce principle. Further from equilibrium, this reduction is extended to a whole class of nonlinear flux-force relations. We show that, when one increases the total production, the entropy production per unit produced starts to increase linearly, as a function of this total production. It is shown which process conditions give an optimum path with an equipartition of the entropy production rate. How this relates to the isoforce principle is discussed. In general constraints on process conditions restrict the freedom to optimize, and therefore make it impossible to realise the most favorable conditions. The importance of the Onsager relations for the systematic description of the optimization is discussed.

In ecology, economy and also in technology we are dealing with open dissipative systems. The long term stability of such systems in either cyclic processes or in stationary states is due to their ability to export their surplus of entropy. For this process valuable low entropy resources are consumed and transformed into waste. This mechanism determines to a large extent the efficiency of open dissipative systems. This is illustrated by selected examples from energy and environmental engineering, biology and global ecology.

The performance of an isothermal combined-cycle chemical engine with mass leak is analyzed in this paper. The relation between optimal power output and efficiency, the maximum power output and the corresponding efficiency, as well as the maximum efficiency and the corresponding power output are derived.