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

The second integral in the previous relation is recognized as the entropy

change S 1 S 2. Therefore,

which can be rearranged as

(7–7)

It can also be expressed in differential form as

(7–8)

where the equality holds for an internally reversible process and the

inequality for an irreversible process. We may conclude from these equa-

tions that the entropy change of a closed system during an irreversible

process is greater than the integral of dQ/Tevaluated for that process. In the

limiting case of a reversible process, these two quantities become equal. We

again emphasize that Tin these relations is the thermodynamic temperature

at the boundarywhere the differential heat dQis transferred between the

system and the surroundings.

The quantity SS 2 S 1 represents the entropy changeof the system.

For a reversible process, it becomes equal to 

2

1 dQ/T, which represents the

entropy transferwith heat.

The inequality sign in the preceding relations is a constant reminder that

the entropy change of a closed system during an irreversible process is

always greater than the entropy transfer. That is, some entropy is generated

or createdduring an irreversible process, and this generation is due entirely

to the presence of irreversibilities. The entropy generated during a process is

called entropy generationand is denoted by Sgen. Noting that the difference

between the entropy change of a closed system and the entropy transfer is

equal to entropy generation, Eq. 7–7 can be rewritten as an equality as

(7–9)

Note that the entropy generation Sgenis always a positivequantity or zero.

Its value depends on the process, and thus it is nota property of the system.

Also, in the absence of any entropy transfer, the entropy change of a system

is equal to the entropy generation.

Equation 7–7 has far-reaching implications in thermodynamics. For an

isolated system (or simply an adiabatic closed system), the heat transfer is

zero, and Eq. 7–7 reduces to

(7–10)

This equation can be expressed as the entropy of an isolated system during

a process always increases or, in the limiting case of a reversible process,

remains constant. In other words, it neverdecreases. This is known as the

increase of entropy principle.Note that in the absence of any heat transfer,

entropy change is due to irreversibilities only, and their effect is always to

increase entropy.

¢Sisolated 0

¢SsysS 2 S 1 

2

1

¬

dQ

T

Sgen

dS

dQ

T

S 2 S 1 

2

1

¬

dQ

T



2

1

¬

dQ

T

S 1 S 2  0

336 | Thermodynamics

Process 1-2

(reversible or

irreversible)

1

2

Process 2-1

(internally

reversible)

FIGURE 7–5

A cycle composed of a reversible and
an irreversible process.