Energy Balance for Closed Systems

If the boundary of a system does not permit the transfer of matter between the system and its surroundings, the system is said to be closed, and its mass is necessarily constant. The development of basic concepts in thermodynamics is facilitated by a careful examination of closed systems, and for this reason they are treated in detail in the following sections. Far more important for industrial practice are processes in which matter crosses the system boundary as streams tliat enter and leave process equipment. Such systems are said to be open, and tliey are treated later in tliis cliapter, once the necessary foundation material lias been presented. 

The choice of signs used witli Q and W depends on wliich direction of transport is regarded as positive. 

A(Eiiergy of surroundings) = Qsmr Wsun- = Equation (2.1) now becomes  

Tliis equation means tliat tlie total energy change of a closed system equals tlie net energy transferred into it as heat and work. 

Closed systems often undergo processes tliat cause no change in the system otlier tlian in its internal energy. For such processes, Eq. (2.2) reduces to  

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Energy Balance for Closed Systems (Fixed Mass)... 

Let us look now at some examples of applications of the energy balance for closed systems. Remember to follow the checklist presented in Chap. 2 in analyzing the problem. 

A system of fixed mass is called a closed system and a system that involves mass transfer across its boundaries j.s called an open system or control volume. The first law of therrtiody-nnmics or the energy balance for any system undergoing any process can be expressed as... 

Below, we apply the energy balances for macroscopic systems. First, we derive the energy balance equation for closed systems (batch reactors) and then for open systems (flow reactors). Microscopic energy balances, used to describe point-to-point temperature variations inside a chemical reactor, are outside the scope of this book. 

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 ... 

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 ... 

A closed system consists of a fixed mass. The total energy E for most systems encountered in practice consists of the internal energy V. This is especially the case for stationary systems since they don t involve any changes in Iheir velocity or elevation during a process. The energy balance relation in that case reduces to... 

The energy balance for a homogeneous closed system of n moles is ... 

Write down the energy balance for a closed system in symbols [Eq. (4.23)1, and apply it to solve energy balance problems. 

Figure 4.12 Terms in the energy balance for a closed system.

Here we take the gas within the piston and cylinder as the system. The energy balance for this closed system is... 

In commercial systems the accuracy of instruments such as fuel and air flow meters is frequently poor due to the type of meter, placement of the meter, initial setup (mol.wt., temperature range, pressure, etc.), or even as the result of erroneous scaling factors. Attempts made to try to determine what instrument or if an instrument is in error by making mass and energy balance calculations are also usually not productive since all of the necessary parameters are usually not available to close a mass and energy balance around the system. For example, waste gas flow volumes are often not measured since they may contain aerosols, solids, or tar-like constituents that can plug or coat flow mefers causing them to fail or to have poor accuracy. 

Work out the energy balance for a throttle valve (Eq, 4.39), using the closed-system form of the first law. Choose as your system 1 kg of material flowing down the line. 

The whole mass m of the system is constant and this closed system, exchanging only heat and volume work with its surroundings, is supposed to be described again by fields (time function) (2.3) and (2.4) added with fields of (positive) masses /ni(t), m2(t) of both constituents 1, 2 respectively. For closed systems (cf. Sects. 1.2, 2.1) the balance of energy (2.1) and entropy inequality (2.2) are valid but now together with the balance of mass... 

A certain amount of heat dQ) must be supplied to or removed from the closed adsorption system of Fig. 1 to maintain system isothermality when the GSE of component i is changed by a differential amount (dni ). By applying the conventional energy balance for the closed system [II], one gets... 

The energy balance for an open system contains all the terms associated with an ener balance for a closed system, but we must also account for the energy change in the system associated with the streams flowing into and out of the system. To accomplish this task, we consider the case of the generic open system illustrated in Figure 2.9. This open system happens to have two streams in and two streams out however, the balances developed here will be true for any number of inlet or outlet streams. 

The first law of thermodynamics states that the total energy in the universe is a constant. Energy balances have been developed for closed systems and for open systems. For example, the integral equation of the first law for a closed system, written in extensive form, is ... 

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