Increase of entropy principle

This equation shows the decrease of exergy principle, which states that the exergy of an isolated system always decreases for irreversible processes, and remains constant for a reversible process. This is similar to the increase of entropy principle, and is a statement of the second law. 

The rate of entropy production cannot be negative however, the changes in entropy of the system may be positive, negative, or zero. For a reversible process, the entropy production becomes zero when the process is internally reversible as well as the heat transfer between the control volume and its surroundings are reversible. The entropy of an isolated system during an irreversible process always increases, which is called the increase of entropy principle. The energy (power) dissipated because of irreversibility would be... 

Perhaps also friction and wear are related in some distinct manner to the increase of entropy principle of the Second Law of Thermodynamics. While such a relationship may yield no further physical insight into the nature of wear itself, it would surely provide a worthwhile unifying influence hy now including wear and surface deterioration as part of the natural progression from order to randomness in the universe. 

It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not seem to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium (my italics). ... 

In this case there is an increase of entropy in an irreversible process, whilst the energy remains constant. This result brings out clearly the independence of the two fundamental principles of thermodynamics, the first law dealing with the energy of a system of bodies, and the second law with the entropy. 

If one now chooses x, = S and recalls that the xi (k < n) are fieely adjustable, the Second Law would be violated if S were also adjustable at will (by means of non-static adiabatic transitions). Taking continuity requirements into account, it follows that S can either never decrease or never increase. The single example of the sudden expansion of a real gas shows that it can never decrease. One has the Principle of Increase of Entropy The entropy of an adiabatically isolated system can never decrease. 

The practical applications of the theory just outlined divide themselves into two broad classes (1) Those which are based on the existence and properties of the functions U and S and some others related to them—all "thermodynamic identities being merely the integrability condition for the total differentials of these functions and (2) those which aie based on die Principle of Increase of Entropy the entropy of the actual state of an adiabatically enclosed system being greater than that of any neighboring virtual state. 

In Section 7.1 we discussed the thermodynamic condition for a stable mixture given in the Flory-Huggins equation (Eq. 7.1-6), where AS denotes the increase of entropy due to mixing. This equation is based on Boltzmann s principle stating that the entropy of a... 

In such system the rate of increase of entropy Prigogine theorem. Therefore, the entropy of the system is maximum otherwise, an eventual rising of entropy would cause new fluxes increasing system entropy So is maximum, and the Prigogine theorem is equivalent to the principle of maximum of entropy for the system. 

PRINCIPLE OF THE INCREASE OF ENTROPY MATHEMATICAL STATEMENT OF THE SECOND LAW... 

For a simple reversible chemical reaction, if one path is preferred for the backward reaction, the same path must also be preferred for the reverse reaction. This is called the principle of microscopic reversibility. Time can be measured by reversible, periodic phenomena, such as the oscillations of a pendulum. However, the direction of time cannot be determined by such phenomena it is related to the unidirectional increase of entropy in all natural processes. Some ideal processes may be reversible and proceed in forward and backward directions. 

It follows from [4.6.8ff] that the Interfacicd excess entropy cem in principle be obtained from the temperature dependence of the surface tension. Such experiments require some scrutiny both technically (how to prevent evaporation ) and interpretationally (now to account for the temperature coefficients of chemical potentials at fixed concentrations ). Detailed studies are welcome. However, one striking trend may be mentioned ). Adsorption of (at least some) non-ionics is accompanied by an increase of entropy, whereas for the cationic Cj TMA Br" a decrease is observed. Again, more systematic study seems appropriate, before... 

Many changes which are naturally spontaneous, e.g., expansion of a gas, solution of zinc in copper sulfate, etc., can be carried out, actually or in principle, in a reversible manner. It should be clearly understood that in the latter event the total entropy of the system and its surroundings remains unchanged. There is an increase of entropy only when the change occurs spontaneously and hence irreversibly. 

Adsorption of various ions and molecules on electrodes is favored by their interaction with the electrode surface, and also by the squeezing of adsorbate species out of the solution bulk. The latter phenomenon is induced by the difference in free solvation energies AG between the surface layer and in the bulk of the solution. For positive adsorption, AG < 0, which, in its turn, can be caused by a decrease in enthalpy AH < 0) and by an increase of entropy (A5 > 0) as the adsorbate species pass from the solution bulk to the surface. In principle, electrostatic forces can solely induce the interaction of ions with the electrode surface the coulombic attraction and repulsion should result in positive and negative adsorption, respectively. In addition, at a direct contact... 

Since other products are always formed, Michael used the distribution principle , replacing increase of entropy by chemical neutralisation or neutralisation of energies or affinities . If two unsaturated atoms A and B have unequal affinities for the parts C and D of an addendum, the affinity of A for C being greater than that of B for C, then addition occurs if the affinity of... 

Around 1850, however, the German physicist Rudolf Clausius and the English physicist William Thomson (later Lord Kelvin) independently showed that the concept of energy conservation implied that the work capacity of heat included the actual conversion of heat into work. Clausius and Thomson each independently formulated the limits for energy conversion processes of the second law. In 1865, Clausius postulated the fundamental principle of the constant increase of entropy. 

The principle of the constant increase of entropy (Clausius 1865) is that any irreversible process leads to an increase of entropy in the universe at reversible processes, the entropy in the universe remains unchanged. 

Thermodynamics is a deductive science built on the foundation of two fundamental laws that circumscribe the behavior of macroscopic systems the first law of thermodynamics affirms the principle of energy conservation the second law states the principle of entropy increase. In-depth treatments of thermodynamics may be found in References 1—7. 

The relationship between entropy change and spontaneity can be expressed through a basic principle of nature known as the second law of thermodynamics. One way to state this law is to say that in a spontaneous process, there is a net increase in entropy, taking into account both system and surroundings. That is,... 

This result holds equally well, of course, when R happens to be the operator representing the entropy of an ensemble. Both Tr Wx In Wx and Tr WN In WN are invariant under unitary transformations, and so have no time dependence arising from the Schrodinger equation. This implies a paradox with the second law of thermodynamics in that apparently no increase in entropy can occur in an equilibrium isolated system. This paradox has been resolved by observing that no real laboratory system can in fact be conceived in which the hamiltonian is truly independent of time the uncertainty principle allows virtual fluctuations of the hamiltonian with time at all boundaries that are used to define the configuration and isolate the system, and it is easy to prove that such fluctuations necessarily increase the entropy.30... 

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