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

7–13 ■ ENTROPY BALANCE

The property entropyis a measure of molecular disorder or randomness of
a system, and the second law of thermodynamics states that entropy can
be created but it cannot be destroyed. Therefore, the entropy change of
a system during a process is greater than the entropy transfer by an
amount equal to the entropy generated during the process within the system,
and the increase of entropy principlefor any system is expressed as
(Fig. 7–57)

or

(7–68)

which is a verbal statement of Eq. 7–9. This relation is often referred to as
the entropy balance and is applicable to any system undergoing any
process. The entropy balance relation above can be stated as:the entropy
change of a system during a process is equal to the net entropy transfer
through the system boundary and the entropy generated within the system.
Next we discuss the various terms in that relation.

SinSout
Sgen¢Ssystem

°

Total

entropy

entering

¢°

Total

entropy

leaving

¢
°

Total

entropy

generated

¢°

Change in the

total entropy

of the system

¢

Chapter 7 | 377

or

(b) The actual exit temperature of the air is higher than the isentropic exit

temperature evaluated above and is determined from

or

That is, the temperature is 16 K higher at the exit of the actual nozzle as a

result of irreversibilities such as friction. It represents a loss since this rise in

temperature comes at the expense of kinetic energy (Fig. 7–56).

(c) The actual exit velocity of air can be determined from the definition of

isentropic efficiency of a nozzle,

hN

V 22 a

V 22 s

¬S¬V 2 a 2 hNV 22 s 2 0.92 1 666 m>s 22 639 m/s

0.92

950 T 2 a

950  748

¬S¬T 2 a764 K

hN

h 1 h 2 a

h 1 h 2 s



cp,avg 1 T 1 T 2 a 2

cp,avg 1 T 1 T 2 s 2

666 m/s



B

21 1.099 kJ>kg#K 231950  7482 K4a

1000 m^2 >s^2

1 kJ>kg

b

V 2 s 221 h 1 h 2 s 2  22 cp,avg 1 T 1 T 2 s 2

950 K

AIR

Actual nozzle

Isentropic nozzle 748 K, 666 m/s

764 K, 639 m/s

FIGURE 7–56

A substance leaves actual nozzles at a

higher temperature (thus a lower

velocity) as a result of friction.

SystemSystem

∆Esystemsystem

∆Esystem system = = Ein in – Eoutout

∆Ssystem system = = Sin in – Sout out + + Sgengen

Einin Eoutout

Sinin Soutout

∆Ssystemsystem

Sgen gen ≥ 0 0

FIGURE 7–57

Energy and entropy balances for a

system.

SEE TUTORIAL CH. 7, SEC. 13 ON THE DVD.

INTERACTIVE

TUTORIAL