Page 66 - Entrophy Analysis in Thermal Engineering Systems

58 Entropy Analysis in Thermal Engineering Systems

Denote T R ¼T max /T min as the ratio of the maximum-to-minimum temper-
ature of the cycle, where T max ¼T 3 and T min ¼T 1 , it can be inferred from
Eqs. (5.4) and (5.6) that PR¼CR T R .

5.2.2 Brayton cycle

The Brayton cycle consists of the following processes: adiabatic compression
1!2, isobaric heat addition 2!3, adiabatic expansion 3!4, and isobaric
heat removal. A p-V diagram of the cycle is depicted in Fig. 5.2. For the
Brayton cycle, we have p 2 ¼p 3 , p 4 ¼p 1 , CR¼V 4 /V 2 , and PR¼p 2 /p 4 .
The thermal efficiency of the cycle obeys [5]

T 1
η ¼ 1 (5.7)
T 2
For the adiabatic compression process 1!2, we have
1 1
1 γ 1 γ 1

T 1 p 1 p 4 γ 1
¼ ¼ ¼ PR (5.8)
T 2 p 2 p 2
Substituting Eq. (5.8) into Eq. (5.7) yields
1 1
γ (5.9)
η ¼ 1 PR
A relationship can be established between CR and PR in the Brayton cycle.
Using the relation p 2 V 2 ¼ p 4 V 4 , we write
T 2 T 4
T 4
(5.10)
CR ¼ PR
T 2

Fig. 5.2 A p-V diagram of the Brayton cycle.