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

When the temperature Tis not constant, the entropy transfer during a
process 1-2 can be determined by integration (or by summation if appropri-
ate) as

(7–72)

where Qkis the heat transfer through the boundary at temperature Tkat loca-
tion k.
When two systems are in contact, the entropy transfer from the warmer
system is equal to the entropy transfer into the cooler one at the point of
contact. That is, no entropy can be created or destroyed at the boundary
since the boundary has no thickness and occupies no volume.
Note that workis entropy-free, and no entropy is transferred by work.
Energy is transferred by both heat and work, whereas entropy is transferred
only by heat. That is,

Entropy transfer by work: (7–73)

The first law of thermodynamics makes no distinction between heat transfer
and work; it considers them as equals. The distinction between heat transfer
and work is brought out by the second law:an energy interaction that is
accompanied by entropy transfer is heat transfer, and an energy interaction
that is not accompanied by entropy transfer is work. That is, no entropy is
exchanged during a work interaction between a system and its surroundings.
Thus, only energy is exchanged during work interaction whereas both
energyand entropyare exchanged during heat transfer (Fig. 7–59).

2 Mass Flow

Mass contains entropy as well as energy, and the entropy and energy con-
tents of a system are proportional to the mass. (When the mass of a system
is doubled, so are the entropy and energy contents of the system.) Both
entropy and energy are carried into or out of a system by streams of matter,
and the rates of entropy and energy transport into or out of a system are
proportional to the mass flow rate. Closed systems do not involve any mass
flow and thus any entropy transfer by mass. When a mass in the amount of
menters or leaves a system, entropy in the amount of ms, where sis the
specific entropy (entropy per unit mass entering or leaving), accompanies it
(Fig. 7–60). That is,

Entropy transfer by mass flow: (7–74)

Therefore, the entropy of a system increases by mswhen mass in the
amount of menters and decreases by the same amount when the same
amount of mass at the same state leaves the system. When the properties of
the mass change during the process, the entropy transfer by mass flow can
be determined by integration from

(7–75)

where Acis the cross-sectional area of the flow and Vnis the local velocity
normal to dAc.

S

#

mass

Ac

srVn dAc¬and¬Smass s dm

¢t

S

#

mass^ dt

Smassms

Swork 0

Sheat

2

1

¬

dQ

T

a

Qk

Tk

Chapter 7 | 379

Entropy is not

transferred

Entropy with work

generation

via friction

FIGURE 7–59

No entropy accompanies work as it

crosses the system boundary. But

entropy may be generated within the

system as work is dissipated into a less

useful form of energy.

Control volume

mh

ms

h

sm

FIGURE 7–60

Mass contains entropy as well as

energy, and thus mass flow into or out

of system is always accompanied by

energy and entropy transfer.