Volume 35, Issue 3

An exact series solution is given for the first-order equation describing delay times in chemical kinetics, especially auto-ignition of fuels, employing the Arrhenius rate factor. Provision is made for both a constant pressure and a constant volume process by means of an index that describes the temperature dependence of the reaction rate. To allow for the common circumstance that the activation temperature is well above the temperature that would be recognised as the onset of combustion, an onset of combustion is defined analogous to the boundary layer theory of Blasius. Exact offset times are tabulated in non-dimensional form. The limitations of a Taylor-series expansion are discussed.

The limit capacity of binary distillation is considered for conventional heat supply to the column bottom and heat removal from the refluxer and for heat supply and removal distributed over the column height. The form of operating line, appropriating to the minimum of irreversible loss for adjusted productivity and limited transfer coefficients, was found. The expression for possible capacity limit of the distillation column was obtained, depending on flow composition and heat and mass transfer coefficients.

Surface tension and excess volume for trimethyl benzene with tetrahydrofuran, tetra chloromethane, and diethyl solfoxide were theoretically predicted with the help of the Prigogine–Flory–Patterson (PFP) model over the entire concentration range at 298.15 K, which has immense sense of applicability in organic separation and synthesis as solvent. Further, we found that computed results are in good agreement with the experimental findings. The results so obtained have been explained on the basis of packing effect and dipolar-dipolar interactions. An attempt has also been made to study the excess thermodynamic functions that measure the extent of molecular interactions involved in the liquid mixture.

A generalized Coleman–Noll procedure for the exploitation of the entropy principle is presented. It is shown that it is able to dismantle some physical properties of nonlocal materials, which do not emerge if one uses the classical procedure. As an application, Korteweg fluids with a scalar internal variable are studied.

In a recent paper the authors proved that the dispersion relation of heat waves along nanowires could allow one to illustrate the difference between different definitions of non-equilibrium temperature. It turns out that, from the practical perspective, one is led to the same conclusions by using both the absolute non-equilibrium temperature and a dynamical non-equilibrium temperature. Starting from these results, in the present paper the propagation of heat waves in core-shell nanowires is analyzed by using the concept of absolute non-equilibrium temperature. It is shown how the wave speed depends on the properties of both media and on their mutual interaction. Some useful information about the system is presented.

We study thermal radiation outside equilibrium. The situation we consider consists of two bodies emitting photons at two different temperatures. We show that the system evolves to a stationary state characterized by an energy current which satisfies a law similiar to the Stefan–Boltzmann law. The magnitude of this current depends on the temperature of the emitters expressed through the difference of the fourth power of these temperatures. The results obtained show how the classical laws governing the thermal radiation at equlibrium can be generalized away from equilibrium situations.

For the first time, the square-well (SW) model is used as a reference system in the thermodynamic variational calculations for liquids. The SW system is taken within the random phase approximation. To apply this approach to simple metals, the local Animalu–Heine model pseudopotential, the Vashishta–Singwi exchange-correlation function, and the Nozieres–Pines exchange-correlation energy are used. Thermodynamics and structure of liquid Na at T = 373 K are studied. We found that there are several areas of the SW parameters where the solution is stable. We chose the best of such areas in which the calculated structure factor is in good agreement with the experimental one. Then the Helmholtz free energy is minimized in this area with respect to the hard-core diameter and the SW depth at the fixed SW width. It was found that the SW variational procedure gives an upper bound of the Helmholtz free energy which is lower than that in the hard-sphere variational procedure, and that the obtained thermodynamic properties are in reasonable agreement with the experiment.

The theory of evolution by natural selection is herein subsumed by the 2nd law of thermodynamics. The mathematical form of evolutionary theory is based on a re-examination of the probability concept that underlies statistical physics. Probability regarded as physical must include, in addition to isoenergic combinatorial configurations, also energy in conditional circumstances. Consequently, entropy as an additive logarithmic probability measure is found to be a function of the free energy, and the process toward the maximum entropy state is found equivalent to evolution toward the free energy minimum in accordance with the basic maxim of chemical thermodynamics. The principle of increasing entropy when given as an equation of motion reveals that expansion, proliferation, differentiation, diversification, and catalysis are all ways for a system to evolve toward the stationary state in its respective surroundings. Intriguingly, the equation of evolution cannot be solved when there remain degrees of freedom to consume the free energy, and hence evolutionary trajectories of a non-Hamiltonian system remain intractable. Finally, when to-and-from flows of energy are balanced between a system and its surroundings, the system is at the Lyapunov-stable stationary state. The principle of maximal energy dispersal, equivalent to the maximal rate of entropy production, gives rise to the ubiquitous characteristics, conventions, and regularities found in nature, where thermodynamics makes no demarcation line between animate and inanimate.

The behavior of entropy of a model isolated system in which there is non-classical heat conduction is considered. Within the thermodynamic formalism developed, expressions are obtained for the entropy flux and source and also for the total entropy of the isolated system. The approach proposed leads to a strictly monotonic dependence of the total entropy on time for the model system considered.

In this article mesoscopic continuum physics is reviewed using generalized coordinates in the context of liquid crystals. A special focus is put on the balance of spin (internal angular momentum). Mesoscopic continuum physics introduces variables describing the micro-structure – like the orientation of crystals – into the domain of the fields, thus treating them equivalently to space. The theory of mesoscopic continuum physics has been reformulated, resulting in more compact equations. In this formulation the balance of spin shows up naturally as component equations of the balance of momentum. This represents an advantage over the standard formulation of mesoscopic continuum physics.

Steady-state flow of an incompressible fluid in parallel pipes can simultaneously satisfy two contradictory extremum principles in the entropy production, depending on the flow conditions. For a constant total flow rate, the flow can satisfy (i) a pipe network minimum entropy production (MinEP) principle with respect to the flow rates, and (ii) the maximum entropy production (MaxEP) principle of Ziegler and Paltridge with respect to the choice of flow regime. The first principle – different to but allied to that of Prigogine – arises from the stability of the steady state compared to non-steady-state flows; it is proven for isothermal laminar and turbulent flows in parallel pipes with a constant power law exponent, but is otherwise invalid. The second principle appears to be more fundamental, driving the formation of turbulent flow in single and parallel pipes at higher Reynolds numbers. For constant head conditions, the flow can satisfy (i) a modified maximum entropy production (MaxEPMod) principle of Županovíc and co-workers with respect to the flow rates, and (ii) an inversion of the Ziegler–Paltridge MaxEP principle with respect to the flow regime. The interplay between these principles is demonstrated by examples.