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

514 | Thermodynamics

Analysis (a) The T-sdiagram of the cycle is shown in Fig. 9–37. The actual

compressor work and turbine work are determined by using the definitions of

compressor and turbine efficiencies, Eqs. 9–19 and 9–20:

Compressor:

Turbine:

Thus,

That is, the compressor is now consuming 59.2 percent of the work pro-

duced by the turbine (up from 40.3 percent). This increase is due to the

irreversibilities that occur within the compressor and the turbine.

(b) In this case, air leaves the compressor at a higher temperature and

enthalpy, which are determined to be

Thus,

and

That is, the irreversibilities occurring within the turbine and compressor

caused the thermal efficiency of the gas turbine cycle to drop from 42.6 to

26.6 percent. This example shows how sensitive the performance of a

gas-turbine power plant is to the efficiencies of the compressor and the

turbine. In fact, gas-turbine efficiencies did not reach competitive values

until significant improvements were made in the design of gas turbines and

compressors.

(c) The air temperature at the turbine exit is determined from an energy bal-

ance on the turbine:

Then, from Table A–17,

Discussion The temperature at turbine exit is considerably higher than that

at the compressor exit (T 2 a
598 K), which suggests the use of regeneration

to reduce fuel cost.

T 4 a
853 K

880.36 kJ>kg

1395.97515.61

wturb,out
h 3 h 4 aSh 4 a
h 3 wturb,out

hth

wnet

qin

210.41 kJ>kg

790.58 kJ>kg

0.266 or 26.6%

wnet
woutwin
515.61305.20
210.41 kJ>kg

qin
h 3 h 2 a
1395.97605.39
790.58 kJ>kg

605.39 kJ>kg¬ 1 and T 2 a
598 K 2

300.19305.20

wcomp,in
h 2 ah 1 Sh 2 a
h 1 wcomp,in

rbw

wcomp,in

wturb,out

305.20 kJ>kg

515.61 kJ>kg

0.592

wturb,out
hTws
 1 0.85 21 606.60 kJ>kg 2 
515.61 kJ>kg

wcomp,in

ws

hC

244.16 kJ>kg

0.80

305.20 kJ>kg

s

T, K

2 s

3

4 a

1

qin

qout

1300

300

2 a

4 s

FIGURE 9–37

T-sdiagram of the gas-turbine cycle
discussed in Example 9–6.