Page 101 - Entrophy Analysis in Thermal Engineering Systems

94 Entropy Analysis in Thermal Engineering Systems

h i
T 4 ¼ T 3 1 η 1 γ (7.34)
exp 1 CR
where CR¼V 4 /V 3 consistent with the definition of the compression ratio;
see Section 5.2.4.
The rate of heat transferred from the high-temperature reservoir to the
air may now be obtained as follows.
2 3
1 γ
1
T R
γ
6 7
_ 6 CR 7
Q ¼ _mc v T 3 T 2 Þ ¼ _mc v T 1 T R 1 (7.35)
ð
6 7
H η
4 5
com
Likewise, an expression can be derived for the rate of heat rejected to the
low-temperature reservoir.
h i
_ 1 γ
ð
Q ¼ _mc p T 4 T 1 Þ ¼ _mc p T 1 T R 1 η T R 1 CR (7.36)
L
exp
_
_
The net power produced by the cycle is the difference between Q and Q .
H L
Hence,
2 3
1 γ
1
T R
γ
6 7
1 γ

6 CR 7
ð ð
_ W net ¼ _mc v T 1 γη T R 1 CR
6 T R 1Þ γ 1Þ7
exp η
4 5
com
(7.37)
The thermal efficiency of the cycle can be obtained using Eqs. (7.35) and
(7.37).
1 γ

1
T R
γ
1 γ CR
ð
ð
ð Þ T R 1Þ γ 1Þ
γη T R 1 CR
exp η
η ¼ com (7.38)
1 γ
1
T R
γ
CR
T R 1
η
com
Illustrative numerical results are presented in Fig. 7.5 for the normalized
power output and the thermal efficiency of the Atkinson cycle varying with
the compression ratio. Like the Brayton and Otto cycles, the maximum