Page 69 - Entrophy Analysis in Thermal Engineering Systems

Most efficient engine 61

1 γ
T 4 V 4 1 γ
¼ ¼ CR (5.19)
T 3 V 3
Eq. (5.19) may be employed to determine an expression for (T 4 /T 1 ). Hence,

T 4 1 γ
(5.20)
¼ T R CR
T 1
A substitution of Eq. (5.20) into Eq. (5.18) yields

T 2 γ 1 γ
¼ T R CR Þ (5.21)
ð
T 1
The thermal efficiency of the cycle may now be obtained upon substituting
Eqs. (5.20) and (5.21) into Eq. (5.17). Hence,
1 γ 1
η ¼ 1 γ T R CR (5.22)
T R T R CRð γ Þ 1 γ

Note that the relation between CR and PR in the Atkinson cycle obeys
1
γ
CR ¼ PR . Thus, an alternative expression for the thermal efficiency is
1 1
γ 1
η ¼ 1 γ T R PR (5.23)
1 γ
T R T R
PR

5.2.5 Diesel cycle

Fig. 5.5 shows a p-V diagram of the Diesel cycle, which consists of the fol-
lowing four processes: adiabatic compression 1!2, isobaric heat addition

Fig. 5.5 A p-V diagram of the Diesel cycle.