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

Chapter 7 | 401

Isentropic process:

where Pris the relative pressureand vris the relative spe-

cific volume. The function s° depends on temperature only.

The steady-flow workfor a reversible process can be

expressed in terms of the fluid properties as

For incompressible substances (vconstant) it simplifies to

The work done during a steady-flow process is proportional

to the specific volume. Therefore,vshould be kept as small

as possible during a compression process to minimize the

work input and as large as possible during an expansion

process to maximize the work output.

The reversible work inputs to a compressor compressing an

ideal gas from T 1 ,P 1 to P 2 in an isentropic (Pvkconstant),

polytropic (Pvnconstant), or isothermal (Pvconstant)

manner, are determined by integration for each case with the

following results:

Isentropic:

Polytropic:

Isothermal: wcomp,inRT ln ¬

P 2

P 1

wcomp,in

nR 1 T 2 T 12

n 1



nRT 1

n 1

ca

P 2

P 1

b

1 n 1 2>n

 1 d

wcomp,in

kR 1 T 2 T 12

k 1



kRT 1

k 1

¬ca

P 2

P 1

b

1 k 1 2>k

 1 d

wrevv 1 P 2 P 12 ¢ke¢pe

wrev

2

1

v dP¢ke¢pe

a

v 2

v 1

b

sconst.



vr 2

vr 1

a

P 2

P 1

b

sconst.



Pr 2

Pr 1

s° 2 s° 1 
R ln ¬

P 2

P 1

The work input to a compressor can be reduced by using

multistage compression with intercooling. For maximum sav-

ings from the work input, the pressure ratio across each stage

of the compressor must be the same.

Most steady-flow devices operate under adiabatic condi-

tions, and the ideal process for these devices is the isentropic

process. The parameter that describes how efficiently a

device approximates a corresponding isentropic device is

called isentropicor adiabatic efficiency. It is expressed for

turbines, compressors, and nozzles as follows:

In the relations above,h 2 aand h 2 sare the enthalpy values at

the exit state for actual and isentropic processes, respectively.

The entropy balance for any system undergoing any

process can be expressed in the general form as

or, in the rate form,as

For a general steady-flow processit simplifies to

S

#

genam

#

eseam

#

isia

Q

#

k

Tk

S

#

inS

#

out¬
¬S

#

gen¬¬dSsystem>dt

SinSout¬
¬ Sgen¬¬¢Ssystem

hN

Actual KE at nozzle exit

Isentropic KE at nozzle exit



V 22 a

V 22 s



h 1 h 2 a

h 1 h 2 s

hC

Isentropic compressor work

Actual compressor work



ws

wa



h 2 sh 1

h 2 ah 1

hT

Actual turbine work

Isentropic turbine work



wa

ws



h 1 h 2 a

h 1 h 2 s

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

REFERENCES AND SUGGESTED READINGS

1.A. Bejan. Advanced Engineering Thermodynamics. 2nd

ed. New York: Wiley Interscience, 1997.

2.A. Bejan. Entropy Generation through Heat and Fluid

Flow. New York: Wiley Interscience, 1982.

3.Y. A. Çengel and H. Kimmel. “Optimization of Expansion

in Natural Gas Liquefaction Processes.”LNG Journal,

U.K., May–June, 1998.

4.Y. Çerci, Y. A. Çengel, and R. H. Turner, “Reducing the

Cost of Compressed Air in Industrial Facilities.”

International Mechanical Engineering Congress and

Exposition, San Francisco, California, November 12–17,

1995.

5.W. F. E. Feller. Air Compressors: Their Installation,

Operation, and Maintenance. New York: McGraw-Hill,

1944.

6.M. S. Moran and H. N. Shapiro. Fundamentals of

Engineering Thermodynamics. New York: John Wiley &

Sons, 1988.

7.D. W. Nutter, A. J. Britton, and W. M. Heffington.

“Conserve Energy to Cut Operating Costs.”Chemical

Engineering, September 1993, pp. 127–137.

8.J. Rifkin. Entropy. New York: The Viking Press, 1980.

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