Principle of entropy

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 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. 

Studies on thermodynamic restrictions on turbulence modeling show that the kinetic energy equation in a turbulent flow is a direct consequence of the first law of thermodynamics, and the turbulent dissipation rate is a thermodynamic internal variable. The principle of entropy generation, expressed in terms of the Clausius-Duhem and the Clausius-Planck inequalities, imposes restrictions on turbulence modeling. On the other hand, the turbulent dissipation rate as a thermodynamic internal variable ensmes that the mean internal dissipation will be positive and the thermodynamic modeling will be meaningful. 

The standard isobaric potential of greenalite—AG°298 717.2 kcal/mol —is appreciably different from the value of 708.662 obtained by Eugster and I-Ming Chou (1973) by the method of comparison of standard enthalpies of layer silicates in conjunction with the principle of entropy additivity, ity. 

It would be expected for polymers in free solution or in the melt, that, in the absence of an interface, there would be on average an equal number of centres of mass of the polymer molecules in each layer. This is in conformity with the principle of entropy maximization. The presence of the interface was introduced by excluding those conformations that cross the interface. The total segment density in each layer was obtained by summing the segment density contributions from all allowed conformations. This was normalized by recalling that far from the interface, the calculated segment density is simply the bulk volume fraction of polymer (v2 0-... 

We emphasize that we did not discover a new or more basically justified axiom of thermodynamics. Namely, the minimum principle of energy is derived from the maximum principle of entropy, and the stability theorems are derived from the minimum principles of energy enthalpy, free energy, and free enthalpy. Thus, we cannot construct an axiomatical approach to thermodynamics by simply adding the stability theorem to the axioms of thermodynamics. 

We start with a formal derivation of the equivalency of the minimum principle of energy and maximum principle of entropy and illustrate subsequently the principle with a few examples in back-breaking work. A more detailed treatment based on the concavity of entropy, dealing with thermodynamic potentials, can be found in the literature [16]. 

If the state point moves down from point P or P, the state point is an isentropic curve, which conflicts with the second law of thermodynamics (principle of entropy increase for any spontaneous process). If the state point moves up, it compresses the... 

The MEF [3, 4] assumes spray formation is a random process that can be described using the principle of entropy maximization subject to a set of global constraints. 

Relationship 1 reflects a universal principle of entropy increase in systems seeking an equilibrium. Consequently, the equilibrium itself is characterized by a maximum of entropy. 

During the last feiv years, CRISS and COBBLE (1) have developed a principle of entropy correspondence for aqueous ions which predicts ionic heat capacities over wide ranges of temperature (0 - 300°). The entropy relations can be summarized as ... 

It is significant to mention here that below T so enantioseparation is enthalpy controlled, and the 7 -enantiomer is eluted first followed by the -enantiomer, while above T[ o enantioseparation is entropy controlled and the reverse order of elution is observed. Therefore, the reverse order of elution occurs due to enthalpy and entropy compensation. Only when the van t Hoff plot is linear over a wide range of temperatures, including Tisoj is the thermodynamic principle of entropy/enthalpy compensation established. In principle, temperature-dependent multimodal recognition mechanisms that oppose each other may also account for the observation of an isoenantioselective temperature [87, 135, 136]. 

Model of Diffusion-Induced Crain Boundary Migration (DICM) Based on the Extremal Principle of Entropy Production by the Example of Cu-Ni Thin Films... 

In summary, the previously given form of the minimal principle of entropy production leads to a class of generalized Onsager constitutive theory, which is also direct generalization of the linear Onsager s theory having their dissipation potentials as homogeneous Euler s functions. 

For us to cause a reduction in entropy in one part of the universe, the principles of entropy, free energy, and equilihrium require that we generate an even greater increase in entropy somewhere else. 

Recently, new interesting phenomena that control the mode of packing of polymers have been found, and it has been shown that the basic principles of polymer crystallography are, in some cases, violated. In particular, (1) an atactic polymer can crystallize this is, for instance, the case of polyacrylonitrile [107] (2) in a crystalline polymer the chains can be nonparallel for instance, the structure of the yform of iPP is characterized by the packing of nearly perpendicular chains [108, 109] (3) the principle of entropy-driven phase formation may be violated and the high local symmetry of the chains is lost in the limit-ordered crystkhne lattice of polymers (symmetry breaking). 

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