Dissipation, of energy

Langevin dynamics simulates the effect of molecular collisions and the resulting dissipation of energy that occur in real solvents, without explicitly including solvent molecules. This is accomplished by adding a random force (to model the effect of collisions) and a frictional force (to model dissipative losses) to each atom at each time step. Mathematically, this is expressed by the Langevin equation of motion (compare to Equation (22) in the previous chapter) ... 

Two approaches to this equation have been employed. (/) The scalar product is formed between the differential vector equation of motion and the vector velocity and the resulting equation is integrated (1). This is the most rigorous approach and for laminar flow yields an expHcit equation for AF in terms of the velocity gradients within the system. (2) The overall energy balance is manipulated by asserting that the local irreversible dissipation of energy is measured by the difference ... 

The term j(t is the rate of dissipation of energy per unit volume by joule heating. This occurs within the working fluid, and so represents a departure... 

Generation of Heat in Electric Fields. One of the practical problems encountered in electrophoresis is the generation of heat from resistive dissipation of energy in the electrophoretic medium. The generation of heat (foule heating) is given by... 

Other theories proposed dissipation of energy through crack interaction localised heating causing the material to be raised to above the glass transition temperature in the layers of resin between the rubber droplets and a proposal that extension causes dilation so that the free volume is increased and the glass transition temperature drops to below the temperature of the polyblend. 

The presence of many crazes is considered to distribute stresses which would otherwise be concentrated at the tip of a few growing cracks. Additionally there is some evidence that when a propagating craze reaches a particle it often divides so that if there is a large number of particles per unit volume there is a high dissipation of energy. 

These apparently paradoxical phenomena have been explained by Andronov 4 from the physical point of view, a major point being that at the two nonanalytic points impulsive inputs of energy occur which compensate for the continuous dissipation of energy on the analytic arcs of convergent spirals33 (compare with the theory of clocks of Section 6.9). 

It follows that all irreversible processes must yield less than the maximum amount of available energy, or that all irreversible processes are attended by dissipation of energy. 

Every irreversible process leads. to dissipation of energy. 

Now if any irreversible changes occur in the system itself during the execution of the cycle, the principle of dissipation of energy shows that the available energy will be diminished in virtue of these, and since the available energy of the system must be the same after as it was before the execution of the cycle, because the state of the system is unaltered, it follows that some available energy must have been absorbed from outside in connection with the absorption of heat hence (A ) and therefore also... 

The application of the principle of entropy to irreversible processes has given rise to much discussion and controversy. The exposition here adopted is based on the investigations of Lord Kelvin (1852) in connexion with Dissipation of Energy. 

Since this is positive, by the principle of dissipation of energy,... 

Loss of motivity (dissipation of energy) is therefore accompanied by increase of entropy, but the two changes are not wholly co-extensive, because the former is less the lower the temperature T0 of the auxiliary medium, whilst the latter is independent of T0, and depends only on the temperature of the parts of the system. If T0 = 0, i.e., the temperature of the surroundings is absolute zero, there is no loss of motivity, whilst the entropy goes on increasing without limit as the heat is gradually conducted to colder bodies. 

The presence of any type of irreversibility inevitably leads to dissipation of energy, and therefore to increase of entropy. 

Criterion (1) is seen to be identical with Horstmann s principle it has been largely employed in the treatment of equilibria by Planck. It is, however, not always convenient in application because the systems which actually occur in practice are not isolated we shall therefore modify the relation so as to make it suitable for non-isolated systems. In this investigation we shall recover the first general method for determining the conditions of equilibrium—the principle of dissipation of energy. 

As soon as we had shown that is an available energy, from the definition of 39 and equation (13a), we could at once have inferred the relations (10)—(12) from the principle of dissipation of energy, for V must be a minimum in stable equilibrium. 

We observe that these criteria could at once have been deduced from the principle of dissipation of energy after we had established that is an available energy, from (13), (17), and (19). Similarly for the conditions referred to [Pg.100]

All the expressions for % — evidently represent the dissipation of energy which occurs when the gases are allowed to mix by diffusion in the specified manner. It follows from the principle of dissipation of energy that work will have to be spent in separating the mixture into its constituents, and, conversely, work should be obtained if the gases are allowed to mix in a suitable manner. The first quantity of work will be a minimum, the latter a maximum, and both equal and opposite, when the processes are conducted reversibly. 

The primary electroviscous effect occurs, for a dilute system, when the complex fluid is sheared and the electrical double layers around the particles are distorted by the shear field. The viscosity increases as a result of an extra dissipation of energy, which is taken into account as a correction factor pi" to the Einstein equation ... 

In the short term (minutes), energy-dependent quenching reflects the buildup of the trans-thylakoid proton gradient. When the ApH is high, there is an increase in the orderly dissipation of energy that protects... 

Brenner, H., Dissipation of energy due to solid particles suspended in a viscous liquid. Phys. Fluids 1, 338-346 (1958). 

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