Page 83 - Advanced thermodynamics for engineers

68 CHAPTER 4 AVAILABILITY AND EXERGY

Solution:
From Rogers and Mayhew tables (Rogers and Mayhew (1994)):

at p ¼ 30 bar; t ¼ 450 C

3
u ¼ 3020 kJ=kg; h ¼ 3343 kJ=kg; v ¼ 0:1078 m =kg; s ¼ 7:082 kJ=kg K
Hence the specific availability at these conditions is
a ¼ u þ p 0 v T 0 s
3
5
¼ 3020 þ 1 10 0:1078 10 308 7:082

¼ 849:5kJ=kg

(i) Change of availability if expanded to 20 bar, 250 C.

From Rogers and Mayhew tables:
at p ¼ 20 bar; t ¼ 250 C

3
u ¼ 2681 kJ=kg; h ¼ 2904 kJ=kg; v ¼ 0:1115 m =kg; s ¼ 6:547 kJ=kg K
The specific availability at these conditions is
a ¼ u þ p 0 v T 0 s
3
5

¼ 2681 þ 1 10 0:1115 10 308 6:547
¼ 675:7kJ=kg
Thus the maximum work that can be obtained by expanding the gas to these conditions is
w max ¼ a 1 a 2 ¼ 849:5 675:7 ¼ 173:8kJ=kg
This could also be evaluated using Eqn (4.12b), giving

w max ¼ Da ¼ h 1 þ v 1 p 0 p 1 h 2 þ v 2 p 0 p 2 T 0 s 1 s 2
2

¼ 3343 2904 þ 0:1078 1 30 10 0:1115 1 20
2
10 308 7:082 6:547

¼ 439 312:6 þ 211:9 164:78 ¼ 173:5kJ=kg
The values obtained by the different approaches are the same to the accuracy of the figures in the
tables.

(ii) Change of availability if expanded to datum level at p 0 ¼ 1 bar; t 0 ¼ 35 C.
3
u ¼ 146:6kJ=kg; h ¼ 146:6kJ=kg; v ¼ 0:1006 10 2 m =kg; s ¼ 0:5045 kJ=kg K:
The specific availability at the dead state is
a ¼ u þ p 0 v T 0 s
3
5
¼ 146:6 þ 1 10 0:001006=10 308 0:5405
¼ 8:7kJ=kg