Page 142 - Advanced thermodynamics for engineers

128 CHAPTER 6 FINITE TIME (OR ENDOREVERSIBLE) THERMODYNAMICS

T H
.
Q H
.
T 1
W H
E H
T 2
.
Q 2
.
T 3
W C
E C
T 4
.
Q C
T C

FIGURE 6.5
Two internally reversible engines in series forming a combined cycle device operating between two reservoirs
at T H and T C .

Let s 1 ¼ T 2 /T 1 and s 2 ¼ T 4 /T 3 , then rearranging Eqns (6.18)–(6.20) gives

T 1 ¼ T H Q _ H C H ; (6.23)

T 2 ¼ Q _ 2 C 2 þ T 3 ; (6.24)
and
T 4 ¼ Q _ C C C þ T C : (6.25)
Also

( ) ( )
Q _ 2 Q _ 2 Q _ C 1 Q _ C
T 3 ¼ T 4 ¼ þ T C ¼ þ T C ; (6.26)
Q _ C Q _ C C C s 2 C C
and
Q _ 2 1 ( Q _ C )
T 2 ¼ þ þ T C : (6.27)
C 2 s 2 C C
Similarly,

" ( )#
Q _ H 1 Q _ 2 1 Q _ C
T 1 ¼ T 2 ¼ þ þ T C : (6.28)
Q _ 2 s 1 C 2 s 2 C C