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 

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The equations of balance for open systems from Clraps. 2 and 5 are summarized here hr Table 7.1 for easy reference. Included are Eqs. (7.1) and (7.2), restricted forms of tire mass balance. These equations are the basis for the themrodynanricanalysis ofprocesses in tlris and the next two clrapters. When combined with themrodynanric property statements, they allow calculation of process rates and system states. 

Energy Balances for Open Systems (without Chemical Reaction)... 

Make the necessary assumptions and approximations to simplify and solve the energy balance for open systems. 

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. 

Energy balance. The overall energy balance for open systems appears as (2.4.15) in 2.4. Here we neglect the boundary energy L/j, and introduce partial molar quantities for each component i, so (2.4.15) becomes... 

In this section, we carry out a general and conceptual analysis of systems that exchange matter and energy with their surroundings in the absence of chemical reactions. We present, conceptually, the general material balance as well as the overall energy balance for open systems under steady-state... 

Another useful form of the energy balance for open systems is for unsteady-state conditions. Unsteady-state is important, for example, in start-up as the equipment warms up. In the case when the inlet and outlet streams stay constant with time, the unsteady-state energy balance becomes ... 

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