Open systems energy conservation

Virst law. This is the law of conservation of energy which states that the flow of energy into a system must equal the flow of energy out of the same system minus the energy that remains inside the system boundary. For an open system in which the energy flows are not time dependent and in which there is no accumulation of energy in the system, the first law may be written as... 

An open system is one which exchanges mass with its surroundings in addition to exchanging energy. For open systems, the first law is formulated from a consideration of the conservation of energy principle which can be stated as follows ... 

Semibatch or semiflow processes are among the most difficult to analyze from the viewpoint of reactor design because one must deal with an open system under nonsteady-state conditions. Hence the differential equations governing energy and mass conservation are more complex than they would be for the same reaction carried out batchwise or in a continuous flow reactor operating at steady state. 

No laws of physics or thermodynamics are violated in such open dissipative systems exhibiting increased COP and energy conservation laws are rigorously obeyed. Classical equilibrium thermodynamics does not apply and is permissibly violated. Instead, the thermodynamics of open systems far from thermodynamic equilibrium with their active environment—in this case the active environment-rigorously applies [2-4]. 

In a hypothetical system for modeling kinetics, the microscopic cells must be open systems. It is useful to consider entropy as a fluxlike quantity capable of flowing from one part of a system to another, just like energy, mass, and charge. Entropy flux, denoted by Js, is related to the heat flux. An expression that relates Js to measurable fluxes is derived below. Mass, charge, and energy are conserved quantities and additional restrictions on the flux of conserved quantities apply. However, entropy is not conserved—it can be created or destroyed locally. The consequences of entropy production are developed below. 

When the electronic system is open the energy levels acquire a finite lifetime, and the the transitions no longer conserve the sum of electronic and radiation energies. Nonetheless, the radiation introduces again a unique effect, which goes beyond that of the Debye-Waller exponent. [11] Imagine an... 

In principle, Equation (3.5) represents an infinite set of coupled equations. In practice, however, we must truncate the expansion (3.4) at a maximal channel n which turns (3.5) into a finite set that can be numerically solved by several, specially developed algorithms (Thomas et al. 1981). The required basis size depends solely on the particular system. The convergence of the close-coupling approach must be tested for each system and for each total energy by variation of n until the desired cross sections do not change when additional channels are included. Expansion (3.4) should, in principle, include all open channels (k > 0) as well as some of the closed vibrational channels (k% < 0). Note, however, that because of energy conservation the latter cannot be populated asymptotically. 

Most of the chemical reactions run in laboratory courses are to be performed in open systems. This means that there won t be a build-up of pressure and some work will be done by the reacting system on the surroundings or, possibly, by the surroundings on the system. In such cases, the principle of conservation of energy requires that the amount of heat shifted must adjust itself to provide for the small, but significant, amount of this work. A new function, the enthalpy, H, can be defined which is related simply to the heat flow in an open or constant-pressure vessel by the definition, H = E + PV. The amount of heat absorbed (or released) in a constant-pressure process is exactly equal to AH, the increase (or decrease) in H. 

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. 

In Chap. 2 the first law of thermodynamics was applied to closed systems (nonflo processes) and to single-stream, steady-state flow processes to provide specifi equations of energy conservation for these important applications. Our purpos here is to present a more general equation applicable to an open system or to control volume. 

The general form of the mechanical energy balance can be derived starting with the open-system balance and a second equation expressing the law of conservation of momentum, a derivation beyond the scope of this book. This section presents a simplified form for a single incompressible liquid flowing into and out of a process system at steady state. 

Although the focus of the preceding sections has beenon closed systems, the concepts presented find far more extensive application. The laws of mass and energy conservation apply to all processes, to open as well as to closed systems. Indeed, the open system includes the closed system as a special case. The remainder of this chapter is therefore devoted to the treatment of open systems and thus to the development of equations of wide applicability. 

The region of space identified for analysis of open systems is called a control volume it is separated from its surroundings by a control surface. The fluid witliin the control volume is the themiodynamic system for wliich mass and energy balances are written. The control volume shown schematically in Fig. 2.5 is separated from its surroundings by an extensible control surface. Two streams with flow rates rh i and m2 are shown directed into the control volume, and one stream with flow rate m3 is directed out. Since mass is conserved, the rate of change of mass witliin the control volume, dm ldt, equals the net rate of flow of mass into the control volume. Tire convention is that flow is positive when directed into the control volume and negative when directed out. Tire mass balance is expressed mathematically by ... 

It is apparent from the above considerations that the external energy E plays a role in this approach. With respect to the eigenstates of H , the system is open. Energy conservation principle brings the description into the realm of thermodynamics. The inclusion of the kinetic energy related to the inertial frame used to unfold H is then required by energy conservation. 

The steady-state ma.ss balance equation for the open system consisting of the device and its contents is cIN/cIi = 0 = /Vj. = /V -f, Vi + N, . Since, from the problem statement. /Vi = yV = — j/V. mass is conserved. The steady-state energy balance for this device is... 

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. 

A term describing the transport across the boundaries is called flux, and the creation of any extensive quantity within the system is called production. Immediately, one recognizes that the conservation laws of mass and energy, which is discussed in Sect. 2.1.2, forbid their production. A final set of new terms is also shown in Fig. 2.16. It is a classification of the types of systems. The first type is an open system, represented by an open container, for example, as used for the sample placement in thermogravimetry. In such a system mass and energy flux may occur... 

Based on the laws of conservation of mass, energy and momentum, balance equations are set up [1.1] -[1.5]. For a general open system... 

Based on the law of conservation of energy, an energy balance analogous to the material balance may be set up for any bounded balance area. Using the terms from Fig. 1-7 for the energetic and materialistic open system, the energy balance becomes... 

Define these terms system, surroundings, open system, closed system, isolated system, thermal energy, chemical energy, potential energy, kinetic energy, law of conservation of energy. 

The first law of fhermodynamics, which predates the theory of relativity, states that the total quantity of energy is conserved. It is convenient to treat energy released from nuclear reactions as a volumetric heat generation source term and include it with heat transferred into the system. For an open system (see Figure 23.2) undergoing a transient, the first law may be written... 

Energy Equation (Conservation of Energy, First Law of Thermodynamies for an Open System)... 

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