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

or, in the rate form, as

(7–83)

This entropy balance relation can be stated as:

The rate of entropy change within the control volume during a process is

equal to the sum of the rate of entropy transfer through the control volume

boundary by heat transfer, the net rate of entropy transfer into the control

volume by mass flow, and the rate of entropy generation within the

boundaries of the control volume as a result of irreversibilities.

Most control volumes encountered in practice such as turbines, compres-

sors, nozzles, diffusers, heat exchangers, pipes, and ducts operate steadily,

and thus they experience no change in their entropy. Therefore, the entropy

balance relation for a general steady-flow processcan be obtained from Eq.

7–83 by setting dSCV/dt0 and rearranging to give

Steady-flow: (7–84)

For single-stream(one inlet and one exit) steady-flow devices, the entropy

balance relation simplifies to

Steady-flow, single-stream: (7–85)

For the case of an adiabaticsingle-stream device, the entropy balance rela-

tion further simplifies to

Steady-flow, single-stream, adiabatic: (7–86)

which indicates that the specific entropy of the fluid must increase as it

flows through an adiabatic device since S

.

gen0 (Fig. 7–64). If the flow

through the device is reversible and adiabatic, then the entropy remains

constant,sesi, regardless of the changes in other properties.

S

#

genm

#

1 sesi 2

S

#

genm

# 1 s

esi^2 a

Q

#

k

Tk

S

#

genam

#

eseam

#

isia

Q

#

k

Tk

a

Q

#

k

Tk

am

#

isiam

#

ese
S

#

gendSCV>dt¬¬^1 kW>K^2

382 | Thermodynamics

se > si

si

FIGURE 7–64

The entropy of a substance always
increases (or remains constant in the
case of a reversible process) as it flows
through a single-stream, adiabatic,
steady-flow device.

EXAMPLE 7–17 Entropy Generation in a Wall

Consider steady heat transfer through a 5-m 7-m brick wall of a house of

thickness 30 cm. On a day when the temperature of the outdoors is 0C, the

house is maintained at 27C. The temperatures of the inner and outer

surfaces of the brick wall are measured to be 20C and 5C, respectively, and

the rate of heat transfer through the wall is 1035 W. Determine the rate of

entropy generation in the wall, and the rate of total entropy generation

associated with this heat transfer process.

Solution Steady heat transfer through a wall is considered. For specified

heat transfer rate, wall temperatures, and environment temperatures, the

entropy generation rate within the wall and the total entropy generation rate

are to be determined.

Assumptions 1 The process is steady, and thus the rate of heat transfer

through the wall is constant. 2 Heat transfer through the wall is one-

dimensional.