Energy,balance for an open system

In Section 7.4a we outline the calculation of the work (or more precisely, the rate of energy transferred as work) required to move fluid through a continuous process system, and in Section 7.4b we review the concepts of intensive and extensive variables introduced in Chapter 6 and introduce the concept of specific properties of a substance. Section 7.4c uses the results of the two preceding sections to derive the energy balance for an open system at steady state. 

When writing an energy balance for an open system at steady state, first simplify Equation 7.4-15 by dropping negligible terms, then solve the simplified equation for whichever variable cannot be determined independently from other information in the process description. 

The unsteady-state energy balance for an open system that has n species, each entering and leaving the system at its respective molar flow rates Fi (moles of i per time) and with its respective energy (joules per mole of i), is... 

Write down the energy balance for an open system [Eq. (4.24)] in words and symbols, explain each term, and apply the equation to... 

Write down the steady-state mechanical energy balance for an open system and apply it to a problem. 

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. 

We will begin by writing the general energy balance for an open system liF -... 

Table 2.3 demonstrates the impact of the various thermodynamic paths on a total energy balance for an open system. For the isenthalpic case, AT = 0 for an ideal gas since the enthalpy is a function of temperature only. For the isentropic case, Q = 0 since dS = dQ/T. For the isothermal case, AH = 0 since the enthalpy for an ideal gas is a function of temperature only. For the adiabatic case, AS = 0 for a reversible process only. For both the isentropic and adiabatic cases, the shaft work determined is a maximum for reversible processes. 

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. 

Define the terms flow work, shaft work, specific internal energy, specific volume, and specific enthalpy. Write the energy balance for an open process system in terms of enthalpy and shaft work and state the conditions under which each of the five terms can be neglected. Given a description of an open process system, simplify the energy balance and solve it for whichever term is not specified in the process description. 

For an open system with energy exchange across its boundaries, as shown in Fig. 1.20, the energy balance can be written as... 

Given a description of any nonreactive process for which tabulated specific internal energies or specific enthalpies are available at all input and output states for all process species, (a) draw and completely label a flowchart, including Q and W (or Q and for an open system) if their values are either specified or called for in a problem statement (b) perform a degree-of-freedom analysis and (c) write the necessary equations (including the appropriately simplified energy balance) to determine all requested variables. 

We have seen that for an open system in which shaft work and kinetic and potential energy changes can be neglected, the energy balance reduces to... 

For an open system at steady state with negligible kinetic and potential energy changes from inlet to outlet and no energy transfer as shaft work, the balance is... 

Finally, we may substitute the expressions of Equations 11.3-3 through 11.3-11 into the general energy balance (Equation 11.3-2) to obtain for an open system... 

This is precisely the form of the first law for a closed system of constant volume that exchanges heat and shaft work with the surroundings (see eg. r. oll The reason that the PFwork does not appear here is that the form of the energy balance in eg. (6.i7l implicitly assumes that the system has constant volume, i.e., its boundaries are rigid and thus the system is prevented from exchanging any PF work. For an open system with movable boundaries (a rubber balloon, for example), eg. (6.17) must be amended to include PFwork in addition to any shaft work. 

The energy balance is the result of the first law of thermodynamics. For an open system all kinds of environmental influences should be taken into account. 

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. 

Given fluid conditions (pressure, flow rate, velocity, elevation) at the inlet and outlet of an open system and values of friction loss and shaft work within the system, substitute known quantities into the mechanical energy balance (or the Bernoulli equation if friction loss and shaft work can be neglected) and solve the equation for whichever variable is unknown. 

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... 

We begin with the application of the first law of thermodynamics first to a dosed system and then to an open system. A system is any bounded portion of the universe, moving or stationary, which is chosen for the application of the various thermodynamic equations. For a closed system, in which no mass crosses the system boundaries, the change in total energy of the system, dE, is equal to the heat flow to the system. 8Q. minus the work done by the system on the surroundings. W. For a closed sy.sreni. the energy balance is... 

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. 

This equation gives the general unsteady-state energy balance equation in an open system. It is often referred to as the form of the first law for open systems. Below we consider a number of special cases. 

The CSTR is an open system exchanging mass and energy with its environment. It is said to achieve a steady state whenever its state variables are invariant in time this is also often referred to as a fixed-point solution. Under such conditions, the transient balance for each chemical component in the... 

An energy balance for the sample side of the calorimeter (open system, //out = 0. no shaft work) yields [11] ... 

The fluxes of mass and energy required in expression 8.7 can be obtained from the equation of continuity per volume unit and energy balance, respectively, for an open unsteady state multicomponent system. Let (a) be a given phase, then the fundamental equation of continuity is given by convective, diffusive and chemical reaction contributions. 

Some models assume that a system reaches a steady state rather than equilibrium. Equilibrium is defined by the principle of detailed balance, which requires that the forward and reverse rates are equal and that each step along the reaction path is reversible. The forward and reverse rates of steady-state processes are equal but the process steps that produce the forward rate are different from those that produce the reverse rate. At steady state, the state variables of an open system remain constant even though there is mass and/or energy flow through the system. The steady-state assumption is especially useful for processes that occur in a series, because the concentrations of intermediates that are formed and subsequently destroyed are constant. Perturbation of a steady-state system produces a transient state where the state variables evolve over time and approach a new steady state asymptotically. 

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