Entropy balance for open systems

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 flow rate m molar flow rate ft volumetric flow rate velocity  

ENERGY, AND ENTROPY BALANCES FOR OPEN SYSTEMS 

Mass and energy balances for an open system are written with respect to a region of space known as a control volume, bounded by an imaginary control. surface that separates it from the surroundings. This surface may follow fixed walls or be arbitrarily placed it may be rigid or flexible. 

Mass Balance for Open Systems Because mass is conserved, the time rate of change of mass within the control volume equals the net rate of flow of mass into the control volume. The flow is positive when directed into the control volume and negative when directed out. The mass balance is expressed mathematically by 

Let rate of heat transfer Qj with respect to a particular part of the control surface be associated with Tt,j where subscript a, j denotes a temperature in the surroundings. The rate of entropy change in the surroundings as a result of this transfer is then —Qj /Taj. The minus sign converts Qj, defined with respect to the system, to a heat rate with respect to the surroundings. The third term in Eq. (5.20) is therefore the sum of all such quantities  

The final term, representing the rate of entropy generation Sq, reflects the second-law requirement that it be positive for irreversible processes. There are two sources of irreversibility (a) those within the control volume, i.e., internal irreversibilities,and (b) those resultingfrom heat transfer across finite temperature differences between system and surroundings, i.e., external thermal irreversibilities. In the limiting case where Sq = 0, the process must be completely reversible, implying  

The second item means either that heat reservoirs are included in the surroundings with temperatures equal to those of the control surface or that Carnot engines are interposed in the surroundings between the control-surface temperatures and the heat-reservoir temperatures. 

For a steady-state flow process tire mass and entropy of the fluid in the control volume are constant, and d mS /dt is zero. Equation 27 then becomes  

If in addition there is but one entrance and one exit, with m the same for both streams, dividing tljrougli by tit yields  

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

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 designation reversible arises from the following observation. Consider the change in state of a general system open to the flow of mass, heat, and work, Between two equal tiTne intervals, 0 to t and to f2, where t2 = 2t. The mass, energy, and entropy balances for this system are, from Eqs. 2.2-4, 3.1-6, and 4.1-9,... 

Entropy balance. The open-system entropy balance appears in (2.4.21). Again, we neglect the boundary term and introduce partial molar entropies for each component, so (2.4.21) becomes... 

For open systems, the first and second laws are particular forms of the general stuff equation presented in 1.4. The first law represents an energy balance on a system, and it asserts that energy is a conserved quantity. Similarly, the second law represents an entropy balance, but the second law asserts that entropy is not conserved through the actions of dissipative forces, entropy is created (but never consumed) during any irreversible process. 

The rate form of entropy balances for closed and open systems are... 

Entropy balances have been developed for closed systems and for open systems. In each case, we account for the entropy change of the universe by adding together the entropy change for the system and the entropy change for the surroundings. For example, the integral equation of the second law for a closed system, written in extensive form, is ... 

First of all, we will touch a widely believed misunderstanding about impossibility of using the second law of thermodynamics in the analysis of open systems. Surely, the conclusion on inevitable degradation of isolated systems that follows from the second law of thermodynamics cannot be applied to open systems. And particularly unreasonable is the supposition about thermal death of the Universe that is based on the opinion of its isolation. The entropy production caused by irreversible energy dissipation is, however, positive in any system. Here we have a complete analogy with the first law of thermodynamics. Energy is fully conserved only in the isolated systems. For the open systems the balance equalities include exchange components which can lead to the entropy reduction of these systems at its increase due to internal processes as well. 

Entropy balance, also called the second law of thermodynamics, for an open system... 

A second procedure, using the methods of thermodynamics applied to Irreversible processes, offers another new approach for understanding the failure of materials. For example, the equilibrium thermodynamics of closed systems predicts that a system will evolve In a manner that minimizes Its energy (or maximizes Its entropy). The thermodynamics of Irreversible processes In open systems predicts that the system will evolve In a manner that minimizes the dissipation of energy under the constraint that a balance of power Is maintained between the system and Its environment. Application of these principles of nonlinear Irreversible thermodynamics has made possible a formal relationship between thermodynamics, molecular and morphological structural parameters. 

For the generic, open, nonreacting system represented schematically in Figure 3.7, an expression for Q is obtained by rearranging the entropy balance (3.6.10),... 

The interface itself has negligible mass compared to the masses of the phases, and during processes, states of the interface may be undefined or undefinable. We will treat the interface as an open system and interpret each phase as a "port" for the other phase that is, the open-system energy and entropy balances from 2.4 will apply. In what follows, we first derive the combined first and second laws ( 7.2.1). Then we find limits on the directions ( 7.2.2) and magnitudes ( 7.2.3) of mass and energy transfers between phases a and p. 

Develop the balance equation for energy and entropy in open systems. 

Generally, for an open thermodynamic system and its environment with which it has an exchange of matter, one can write the balance equation for the global variation of entropy [9-12]. 

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