barcode generator vb.net code Entropy Balance for Open Systems in Software

Generation QR in Software Entropy Balance for Open Systems

The statement of balance, expressed as rates, is therefore:

1 1 i;i5 1 [ 1 1

where sGis the rate of entropy generation This equation is the general rate form of the entropy balance, applicable at any instant Each term can vary with time The first term is simply the net rate of gain in entropy of the flowing streams, ie, the difference between the total entropy transported out by exit streams and the total entropy transported in by entrance streams The second term is the time rate of change of the total entropy of the fluid contained within the control volume The third term accounts for entropy changes in the surroundings, the result of heat transfer between system and surroundings Let rate of heat transfer Q, with respect to a particular part of the control surface be associated with T,,j where subscript a, j denotes a temperature in the surroundings The rate of entropy change in the surroundings as a result of this transfer is then - Q j / ~ uj, The minus sign converts Q j, defined with respect to the system, to a heat rate with respect to the surroundings The third term in Eq (520) is therefore the sum of all such quantities:

Equation (520) is now written:

The final term, representing the rate of entropy generation sG, reflects the second-law requirement that it be positive for irreversible processes There are two sources of irreversibility: ( a ) those within the control volume, ie, internal irreversibilities, and ( b ) those resulting from heat transfer across finite temperature differences between system and surroundings, ie, external thermal irreversibilities In the limiting case where sG= 0 , the process must be completely reversible, implying: The process is internally reversible within the control volume Heat transfer between the control volume and its surroundings is reversible The second item means either that heat reservoirs are included in the surroundings with temperatures equal to those of the control surface or that Carnot engines are interposed in the surroundings between the control-surface temperatures and the heat-reservoir temperatures

For a steady-state flow process the mass and entropy of the fluid in the control volume are constant, and d(mS),,/dt is zero Equation (521) then becomes:

If in addition there is but one entrance and one exit, with m the same for both streams, dividing through by m yields:

In any steady-state flow process requiring work, there is an absolute minimum amount which must be expended to accomplish the desired change of state of the fluid flowing through the control volume In a process producing work, there is an absolute maximum amount which may be accomplished as the result of a given change of state of the fluid flowing through the control volume In either case, the limiting value obtains when the change of state associated with the process is accomplished completely reversibly For such a process, the entropy generation is zero, and Eq (522), written for the uniform surroundings temperature T,, becomes:

Substitute this expression for Q in the energy balance, Eq (230):

+ $ u2 + zg) m]f, = T,

A(Sm)f, i- wS (rev)

The shaft work, rev), is here the work of a completely reversible process If given the name ideal work, wideal, the preceding equation may be rewritten:

In most applications to chemical processes, the kinetic- and potential-energy terms are negligible compared with the others; in this event Eq (524) reduces to:

(525)

For the special case of a single stream flowing through the control volume, Eq (525) becomes: Wideal= m ( A H - T, AS) Division by m puts this equation on a unit-mass basis: Widea = A H - To A s A completely reversible process is hypothetical, devised solely for determination of the ideal work associated with a given change of state The only connection between the hypothetical reversible process and an actual process is that it brings about the same change of state as the actual process Our objective is to compare the actual work of a process with the work of the hypothetical reversible process No description is ever required of hypothetical processes devised for the calculation of ideal work One need only realize that such processes may always be imagined Nevertheless, an illustration of a hypothetical reversible process is given in Ex 57 Equations (524) through (527) give the work of a completely reversible process associated with given property changes in the flowing streams When the same property changes occur in an actual process, the actual work W, (or W,) as given by an energy balance, can be compared with the ideal work When Wideal(or Wideal) positive, it is the minimum work is required to bring about a given change in the properties of the flowing streams, and is smaller than wS this case a thermodynamic efficiency q, is defined as the ratio of the ideal work to In the actual work: Wideal qt (work required) = w s

(526)

When wideal (or Wideal) negative, ( wideal 1 is the maximum work obtainablefrom a given change is in the properties of the flowingstreams, and is larger than I W, 1 In this case, the thermodynamic efficiency is defined as the ratio of the actual work to the ideal work: W s qt(work produced) = Wideal