Entropy, increase

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

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 second law reqmres that the entropy of an isolated system either increase or, in the limit, where the system has reached an equilibrium state, remain constant. For a closed (but not isolated) system it requires that any entropy decrease in either the system or its surroundings be more than compensated by an entropy increase in the other part or that in the Emit, where the process is reversible, the total entropy of the system plus its surroundings be constant. 

The total rate of entropy increase (in both system and surroundings) as a result of a process is... 

Thermodynamic Analyses of Cycles The thermodynamic quahty measure of either a piece of equipment or an entire process is its reversibility. The second law, or more precisely the entropy increase, is an effective guide to this degree of irreversibility. However, to obtain a clearer picture of what these entropy increases mean, it has become convenient to relate such an analysis to the additional work that is required to overcome these irreversibihties. The fundamental equation for such an analysis is... 

The isentropic sound speed c, differs in principle from the Hugoniot sound speed Cfj because of the entropy increase on the Hugoniot... 

For elastic compression the entropy increase is small and can come only from effects of thermal conduction. Thus, to a very good approximation at low compressions in most materials,... 

Entropy A function of the state of a substance related to order or disorder. The entropy increases as the substance receives heat. 

Here A5inicrn.ii is the entropy increase of the cooling fluid in control surface B due to friction and the heat transfer (Q, in), A5,nu,iii is the entropy created in the metal between the mainstream and the coolant (or metal plus thermal barrier coating if present) due to temperature difference across it, A uxiemai is the entropy increase in the mainstream flow within control surface A before mixing due to heat transfer (Q, out), plus the various entropy increases due to the mixing process itself in control surface C. 

The rate differences result primarily from the lowering of the activation energies, but in a few cases small entropy increases also contribute. The relatively high rate of reaction of 8-bromoquinoline (346) is postulated to be due to hydrogen bonding of the solvent, piperidine, to the nearby azine-nitrogen in the ground state and... 

This leads to what is called the Clausius form of the second law of thermodynamics. No processes are possible whose only result is the removal of energy from one reservoir and its absorption by another reservoir at a higher temperature. On the other hand, if energy flows from the hot reservoir to the cold reservoir with no other changes in the universe, then the same arguments can be used to show that the entropy increases, nr remains constant for reversible processes. Therefore, such energy flows, which arc vciy familiar, are in agreement with the laws of thermodynamics. 

Thus, for constant pressure processes, the entropy increase is written as... 

The second law of thermodynamics states that energy exists at various levels and is available for use only if it can move from a higher to a lower level. For example, it is impossible for any device to operate in a cycle and produce work while exchanging heat only with bodies at a single fixed temperature. In thermodynamics, a measure of the unavailability of energy has been devised and is known as entropy. As a measure of unavailability, entropy increases as a system loses heat, but remains constant when there is no gain or loss of heat as in an adiabatic process. It is defined by the following differential equation ... 

When a substance is heated at constant pressure without change of phase through a temperature rise dr the heat absorbed is Cp dr, where Cp is the molar heat capacity at constant pressure, and the entropy increase is... 

Thus the entropy increase when the substance is heated from r, to T2 is... 

Strategy Consider the relative disorder of final and initial states remember that entropy increases in the order solid < liquid < gas. 

In many physical changes, the entropy increase is the major driving force. This situation applies when two liquids with similar intermolecular forces, such as benzene (C6H< ) and tol-... 

To close this chapter we emphasize that Hie statistical mechanical definition of macroscopic parameters such as temperature and entropy are well designed to describe isentropic equilibrium systems, but are not immediately applicable to the discussion of transport processes where irreversible entropy increase is an essential feature. A macroscopic system through which heat is flowing does not possess a single tempera-... 

A physically acceptable theory of electrical resistance, or of heat conductivity, must contain a discussion of the explicitly time-dependent hamiltonian needed to supply the current at one boundary and remove it at another boundary of the macrosystem. Lacking this feature, recent theories of such transport phenomena contain no mechanism for irreversible entropy increase, and can be of little more than heuristic value. 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

Corollary.—If the volume of a mol of an ideal gas is increased tenfold at constant temperature the entropy increases by... 

Expanding a gas increases the disorder. Hence, entropy increases with the expansion. 

Heating a solid increases the amplitude of vibrations, and hence, the disorder, and entropy increases. 

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

S2 — S is positive when Ma 1 > 1. Thus a normal shock wave can occur only when the flow is supersonic. From equation 4.96, if Mai > 1, then Ma2 < 1, and therefore the flow necessarily changes from supersonic to subsonic. If Mai = 1> Mai — 1 also, from equation 4.96, and no change therefore takes place. It should be noted that there is no change in the energy of the fluid as it passes through a shock wave, though the entropy increases and therefore the change is irreversible. 

FIGURE 7.3 The change in entropy as a sample is heated for a system with a constant heat capacity (O in the range of interest. Here we have plotted AS/C. The entropy increases logarithmically with temperature. 

As expected, the entropy increases as the space available to the gas expands. 

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