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

Isentropic (Pvkconstant):

(7–57a)

Polytropic (Pvnconstant):

(7–57b)

Isothermal (Pvconstant):

(7–57c)

The three processes are plotted on a P-vdiagram in Fig. 7–45 for the
same inlet state and exit pressure. On a P-vdiagram, the area to the left of
the process curve is the integral of vdP. Thus it is a measure of the steady-
flow compression work. It is interesting to observe from this diagram that of
the three internally reversible cases considered, the adiabatic compression
(Pvkconstant) requires the maximum work and the isothermal compres-
sion (Tconstant or Pvconstant) requires the minimum. The work
input requirement for the polytropic case (Pvnconstant) is between these
two and decreases as the polytropic exponent nis decreased, by increasing
the heat rejection during the compression process. If sufficient heat is
removed, the value of napproaches unity and the process becomes isother-
mal. One common way of cooling the gas during compression is to use
cooling jackets around the casing of the compressors.

Multistage Compression with Intercooling

It is clear from these arguments that cooling a gas as it is compressed is desir-
able since this reduces the required work input to the compressor. However,
often it is not possible to have adequate cooling through the casing of the
compressor, and it becomes necessary to use other techniques to achieve
effective cooling. One such technique is multistage compression with inter-
cooling,where the gas is compressed in stages and cooled between each stage
by passing it through a heat exchanger called an intercooler. Ideally, the cool-
ing process takes place at constant pressure, and the gas is cooled to the initial
temperature T 1 at each intercooler. Multistage compression with intercooling
is especially attractive when a gas is to be compressed to very high pressures.
The effect of intercooling on compressor work is graphically illustrated on
P-vand T-sdiagrams in Fig. 7–46 for a two-stage compressor. The gas is
compressed in the first stage from P 1 to an intermediate pressure Px, cooled at
constant pressure to the initial temperature T 1 , and compressed in the second
stage to the final pressure P 2. The compression processes, in general, can be
modeled as polytropic (Pvnconstant) where the value of nvaries between
kand 1. The colored area on the P-vdiagram represents the work saved as a
result of two-stage compression with intercooling. The process paths for single-
stage isothermal and polytropic processes are also shown for comparison.

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

Chapter 7 | 367

P

1

P 2

P 1

Isentropic (n = k)

Polytropic (1 < n < k)

Isothermal (n = 1)

v

FIGURE 7–45

P-vdiagrams of isentropic, polytropic,

and isothermal compression processes

between the same pressure limits.