Energy balance closed system

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

In general, when designing a batch reactor, it will be necessary to solve simultaneously one form of the material balance equation and one form of the energy balance equation (equations 10.2.1 and 10.2.5 or equations derived therefrom). Since the reaction rate depends both on temperature and extent of reaction, closed form solutions can be obtained only when the system is isothermal. One must normally employ numerical methods of solution when dealing with nonisothermal systems. 

Let us suppose that there exists a linear combination of the Larmor frequencies such that a1oj1 -j- a2a>2 Aco where the a< are integers close to one and where Aco is the line width. In this case the F(,) terms of the perturbation induce an exchange of quanta between the two Zeeman subsystems, the energy balance being taken up by the dipole-dipole subsystem. One of the quasi-invariants is thus destroyed but the combination Mjax — M2ja.2 remains constant. As in chemical thermodynamics,19 it is useful here to introduce a reaction coordinate f to characterize the state of the system we then have the relations ... 

For the energy balance in a flow system we therefore assume that we can make an enthalpy balance on the contents of the reactor. We can write the rate of enthalpy generation Aff in any flowing or closed system as... 

The energy balance and individual components are illustrated in Figure 3.1. The energy balance shown in the figure is for an open flow system. For a nonflow (or closed) system, the energy balance would appear as in Figure 3.2. 

The first law of thermodynamics provides a description of the energy balance for a given process the second law provides a criterion for deciding whether or not the process will occur spontaneously. The second law of thermodynamics defines the entropy change (A5, in units of J K l) associated with a change in a closed system in terms of the heat absorbed by the system at constant temperature T ... 

Define the terras closed process system, open process system, isothermal process, and adiabatic process. Write the first law of thermodynamics (the energy balance equation) for a closed process system and state the conditions under which each of the five terms in the balance can be neglected. Given a description of a closed process system, simplify the energy balance and solve it for whichever term is not specified in the process description. 

A system is termed open or closed according to whether or not mass crosses the system boundary during the period of time covered by the energy balance. A batch process system is, by definition, closed, and semibatch and continuous systems are open. 

An integral energy balance may be derived for a closed system between two instants of time. Since energy can neither be created nor destroyed, the generation and consumption terms of the general balance (4.2-1) drop out, leaving... 

In deriving the integral mass balance for a closed system in Section 4.2c we eliminated the input and output terms, since by definition no mass crosses the boundaries of a closed system. It is possible, however, for energy to be transferred across the boundaries as heat or work, so that the right side of Equation 7.3-1 may not be eliminated automatically. As with mass balances, however, the accumulation term equals the final value of the balanced quantity (in this case, the system energy) minus the initial value of this quantity. Equation 7,3-1 may therefore be written... 

Energy Balances on Closed Systems 319 or, if the symbol A is used to signify (final - initial),... 

The enthalpy function is important in the analysis of open systems, as we will show in the next section. It can also be shown, however, that if a closed system expands (or contracts) against a constant external pressure, and are negligible, and the only work done by or on the system is the work of the expansion, then the energy balance equation reduces to Q = AT/. A proof of this statement is required in Problem 7.15. 

In chemical process units such as reactors, distillation columns, evaporators, and heat exchangers, shaft work and kinetic and potential energy changes tend to be negligible compared with heat flows and internal energy and enthalpy changes. Energy balances on such units therefore usually omit the former terms and so take the simple form Q = U (closed system) or Q = AH (open system),... 

The first law of thermodynamics for a closed system (which we will generally refer to as the energy balance) between two instants of time is... 

At this point, you can perform energy balance calculations only for systems in which A / (closed system) or AH (open system) can be neglected and for nonreactive systems involving species for which tables of f/ or H are available. Energy balance procedures for other types of systems are presented in Chapters 8 and 9. 

Write and simplify the closed-system energy balance (Equation 7.3-4) for each of the following processes, and state whether nonzero heat and work terms are positive or negative. Begin by defining the system. The solution of part (a) is given as an illustration. 

If a system expands in volume by an amount AV(m- ) against a constant restraining pressure P(N/m ), a quantity PAV (J) of energy is transferred as expansion work from the system to its surroundings. Suppose that the following four conditions are satisfied for a closed system (a) the system expands against a constant pressure (so that Ap = 0) (b) A k == 0 (c) A p = 0 and (d) the only work done by or on the system is expansion work. Prove that under these conditions, the energy balance simplifies ioQ = A//. 

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