Energy entropy balance

Replacing ds/dt by the entropy balance equation, du/dt by the energy conservation equation, and dpkidt by the mass balance equation, we have... 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

Gyftopoulos, E.P. and Widmer, T.F., "Availability Analysis The Combined Energy and Entropy Balance", Thermodynamics Second Law Analysis, A.C.S. Symposium Series, 122, 61-76, 1980. 

Assuming negligible kinetic and potential energy changes, mass, energy, and entropy balances yield... 

Exergy is a unifying concept of many forms of energy, such as heat, mechanical work, and chemical energy. We can derive the exergy Ex relation from the energy and entropy balances for the composite system shown in Figure 4.15... 

For deriving the exeigy balance for heat and work streams, first we multiply the entropy balance by the temperature T0 and then subtract it from the energy balance, and we obtain... 

The mass energy and entropy balance equations are needed. The rate of change of probability density with time is... 

In the case of a practical heat engine an energy balance and a flow balance are made up based on knowledge of turbine blade, heat exchanger and other characteristics. An exergy account, or entropy balance, then establishes the detail of the losses or irreversibilities. No such losses occur in the equilibrium of Figure A.I. See Figure 2.2 of Barclay (1998). 

The themiodynamics of flow is based on mass, energy, and entropy balances, which have been developed in Chaps. 2 and 5. The application of tliese balances to specific processes is considered in this chapter. The discipline imderlying tlie study of flow is fluid mechanics, which encompasses not only the balances of thermodynamics but also the linear-momentum principle (Newton s second law). This makes fluid mechanics a broader field of study. The distinction between thermodynamics problems and fluid-mechanics problems depends on whether this principle is required for solution. Those problems whose solutions depend only on mass conservation and on the laws of thermodynamics are commonly set apart from the study of fluid mechanics and are treated in courses on thermodynamics. Fluid mechanics then deals with the broad spectmm of problems which require application of the momentum principle. This division is arbitrary, but it is traditional and convenient. 

Our restriction to simple fluids was meant to emphasize general laws and phenomena. For this reason, we did not discuss theories of the surface tension of solids, for which a variety of models have been elaborated. One of the considerations for omitting these was that such tensions cannot be measured, so that a check of the quality is edso impossible. We also consciously excluded the surface tensions of liquid metals, liquid crystals, molten crystals and polymer melts. However, spread and adsorbed polymer layers will be considered in chapter 3 and 4, respectively. For similar reasons, and because most practical applications involve ambient temperatures, we did not extensively discuss critical phenomena, notwithstanding their Intrinsic Interest. Under critical conditions the surface energy - surface entropy balance differs considerably from that at lower temperatures, emphasized in this chapter. 

Mass, Energy, and Entropy Balances for Open Systems. 4-14... 

The thermodynamics of flow encompasses mass, energy, and entropy balances for open systems, i.e., for systems whose boundaries allow the inflow and outflow of fluids. The common measures of flow are as follows ... 

MASS, ENERGY, AND ENTROPY BALANCES FOR OPEN SYSTEMS... 

Summary of Equations of Balance for Open Systems Only the most general equations of mass, energy, and entropy balance appear in the preceding sections. In each case important applications require less general versions. The most common restrictedTcase is for steady flow processes, wherein the mass and thermodynamic properties of the fluid within the control volume are not time-dependent. A further simplification results when there is but one entrance and one exit to the control volume. In this event, m is the same for both streams, and the equations may be divided through by this rate to put them on the basis of a unit amount of fluid flowing through the control volume. Summarized in Table 4-3 are the basic equations of balance and their important restricted forms. 

The Combined Energy and Entropy Balance. Several approaches exist for establishing that availability change and not change in any other property represents the optimum (minimum or maximum) work requirement of a process. One of these approaches is based on a combination of the energy and entropy balances of the process. 

The mass, energy and entropy balances on the liquid in the tank (open system) at any time yields... 

There are now several ways to proceed. The most correct is to use the steam tables, and to use either the energy balance or the entropy balance and do the integrals numerically (since the internal energy, enthalpy, entropy, and the changes on vaporization depend on temperature. This is the method we will use first. Then a simpler method will be considered. 

With this information, we can now use either the energy of the entropy balance to solve the problem. To compare the results, we will use both (with the linear average Cp in the energy balance and the log mean in the entropy balance. First using the energy balance... 

To use eqn. (1) to get final temperatures, need another independent equation relating T/ and T-f. Could do an energy balance around tank 1, as in derivation of eqn. (f) of Illustration 2.5-5. A more direct way is to do an entropy balance around a small fluid element, as in Illustration 3.5-2 and immediately obtain Eqn. (e) of that illustration... 

Subtracting the product of temperature and the entropy balance from the energy balance yields... 

Subtracting T times the entropy balance form the energy balance gives... 

Table 4.1-1 gives several special cases of the entropy balance equation, on both a mass and a molar basis, for situations similar to those considered for the mass and energy balance equations in Tables 2.2-1,3.1-1, and 3.1-2. 

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