Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Entropy Generation, Sgen

Irreversibilities such as friction, mixing, chemical reactions, heat transfer

through a finite temperature difference, unrestrained expansion, nonquasi-

equilibrium compression, or expansion always cause the entropy of a sys-

tem to increase, and entropy generation is a measure of the entropy created

by such effects during a process.

For a reversible process(a process that involves no irreversibilities), the

entropy generation is zero and thus the entropy changeof a system is equal

to the entropy transfer. Therefore, the entropy balance relation in the

reversible case becomes analogous to the energy balance relation, which

states that energy changeof a system during a process is equal to the energy

transferduring that process. However, note that the energy change of a sys-

tem equals the energy transfer for anyprocess, but the entropy change of a

system equals the entropy transfer only for a reversibleprocess.

The entropy transfer by heat Q/Tis zero for adiabatic systems, and the

entropy transfer by mass msis zero for systems that involve no mass flow

across their boundary (i.e., closed systems).

Entropy balance for any systemundergoing any processcan be expressed

more explicitly as

(7–76)

or, in the rate form,as

(7–77)

where the rates of entropy transfer by heat transferred at a rate of Q

.

and

mass flowing at a rate of m

.

are S

.

heatQ

.

/Tand S

.

massm

.

s. The entropy bal-

ance can also be expressed on a unit-mass basisas

(7–78)

where all the quantities are expressed per unit mass of the system. Note that

for a reversible process, the entropy generation term Sgendrops out from all

of the relations above.

The term Sgenrepresents the entropy generation within the system bound-

aryonly (Fig. 7–61), and not the entropy generation that may occur outside

the system boundary during the process as a result of external irreversibili-

ties. Therefore, a process for which Sgen0 is internally reversible, but not

necessarily totallyreversible. The totalentropy generated during a process

can be determined by applying the entropy balance to an extended system

that includes the system itself and its immediate surroundings where exter-

nal irreversibilities might be occurring (Fig. 7–62). Also, the entropy change

in this case is equal to the sum of the entropy change of the system and the

entropy change of the immediate surroundings. Note that under steady con-

ditions, the state and thus the entropy of the immediate surroundings (let us

call it the “buffer zone”) at any point does not change during the process,

and the entropy change of the buffer zone is zero. The entropy change of the

buffer zone, if any, is usually small relative to the entropy change of the sys-

tem, and thus it is usually disregarded.

1 sinsout 2
sgen¢ssystem¬¬ 1 kJ>kg#K 2

S

#

inS

#

out¬
¬S

#

gen¬¬dSsystem>dt¬¬^1 kW>K^2

SinSout¬
¬ Sgen¬¬¢Ssystem¬¬ 1 kJ>K 2

380 | Thermodynamics

MMassass SystemSystem

HeatHeat

MassMass

HeatHeat

∆Ssystemsystem

Sgen gen ≥ 0 0

Sinin Soutout

FIGURE 7–61

Mechanisms of entropy transfer for a
general system.

Immediate

surroundings

SYSTEM

Q

Tsurr

FIGURE 7–62

Entropy generation outside system
boundaries can be accounted for by
writing an entropy balance on an
extended system that includes the
system and its immediate
surroundings.

123

Net entropy transfer

by heat and mass

123

Entropy

generation

123

Change

in entropy

123

Rate of net entropy

transfer by heat

and mass

123

Rate of entropy

generation

123

Rate of change

in entropy