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

Chapter 7 | 369

Assumptions 1 Steady operating conditions exist. 2 At specified conditions,
air can be treated as an ideal gas. 3 Kinetic and potential energy changes are
negligible.
Analysis We take the compressor to be the system. This is a control volume
since mass crosses the boundary. A sketch of the system and the T- sdiagram
for the process are given in Fig. 7–47.
The steady-flow compression work for all these four cases is determined by
using the relations developed earlier in this section:
(a) Isentropic compression with k1.4:

(b) Polytropic compression with n1.3:

(c) Isothermal compression:

(d) Ideal two-stage compression with intercooling (n1.3): In this case, the
pressure ratio across each stage is the same, and its value is

Px 1 P 1 P 221 >^2  31 100 kPa 21 900 kPa 241 >^2 300 kPa

189.2 kJ/kg

wcomp,inRT ln¬

P 2

P 1

 1 0.287 kJ>kg#K 21 300 K 2 ln¬

900 kPa

100 kPa

246.4 kJ/kg



1 1.3 21 0.287 kJ>kg#K 21 300 K 2

1.3 1

¬ca

900 kPa

100 kPa

b

1 1.3 1 2>1.3

 1 d

wcomp,in

nRT 1

n 1

ca

P 2

P 1

b

1 n 1 2>n

 1 d

263.2 kJ/kg



1 1.4 21 0.287 kJ>kg#K 21 300 K 2

1.4 1

¬ca

900 kPa

100 kPa

b

1 1.4 1 2>1.4

 1 d

wcomp,in

kRT 1

k 1

ca

P 2

P 1

b

1 k 1 2>k

 1 d

P, kPa

900

100

Isentropic (k = 1.4)

Polytropic (n = 1.3)

Two-stage

Isothermal

P 2 = 900 kPa

P 1 = 100 kPa

T 1 = 300 K

wcomp

1

AIR

COMPRESSOR

v

FIGURE 7–47

Schematic and P-vdiagram for

Example 7–13.