Page 67 - Entrophy Analysis in Thermal Engineering Systems

Most efficient engine 59

1
γ . Likewise, for the adiabatic expan-
1
From Eq. (5.8), we have T 2 ¼ T 1 PR
1
γ 1
sion process 3!4, we get T 4 ¼ T 3 PR . Substituting these two relations
into Eq. (5.10) gives
2 1
γ (5.11)
CR ¼ T R PR
where T R ¼T 3 /T 1 .
Eliminating PR between Eqs. (5.9) and (5.11) leads to an alternative
expression for the efficiency of the Brayton cycle.

1 γ

2 γ
CR
η ¼ 1 T R (5.12)
5.2.3 Otto cycle

The operation of the Otto cycle on a p-V diagram is shown in Fig. 5.3. The
cycle comprises four processes: adiabatic compression 1!2, isochoric heat
addition 2!3, adiabatic expansion 3!4, and isochoric heat removal
4!1. Thus, for the Otto cycle, we have V 2 ¼V 3 , V 4 ¼V 1 , CR¼V 1 /V 3 ,
and PR¼p 3 /p 1 . The thermal efficiency of the Otto cycle is [5]
T 1
η ¼ 1 (5.13)
T 2
Applying the first law to the adiabatic compression process 1!2 gives
1 γ
V 1
T 1
¼ . Thus, Eq. (5.13) may be rewritten as
T 2
V 2
1 γ
V 1 1 γ
η ¼ 1 ¼ 1 CR (5.14)
V 2

Fig. 5.3 A p-V diagram of the Otto cycle.