Page 62 - Advanced thermodynamics for engineers

46 CHAPTER 3 ENGINE CYCLES AND THEIR EFFICIENCIES

(a) (b) (c) (d)
Hot Cold
Compression reservoir Expansion reservoir

FIGURE 3.12
Method of achieving air-standard cycle for Otto cycle. (a) compression (b) heat addition (combustion)
(c) expansion (d) heat extraction (gas exchange).
The basic Otto cycle is made up of four processes:
• Isentropic compression;
• Constant volume heat addition;
• Isentropic expansion and
• Constant volume heat rejection.
These can be depicted on T–s and p–V diagrams as shown in Fig. 3.13.
Since all the processes in Fig. 3.13 are reversible, the areas of the diagrams (a and b) are equal, and
depict the work done in the cycle. The work done is
Z 2 Z 4
I
W ¼ pdV ¼ pdV þ pdV
1 3 (3.13)
p 1 V 1 p 2 V 2 p 3 V 3 p 4 V 4 mR
¼ þ ¼ fðT 1 T 2 ÞþðT 3 T 4 Þg
k 1 k 1 k 1
The energy added to the cycle is that added at constant volume between 2 and 3, and is given by

mR
Q 23 ¼ mc v T 3 T 2 ¼ T 3 T 2 (3.14)
k 1
Hence the thermal efficiency is
I
pdV
ðT 1 T 2 ÞþðT 3 T 4 Þ ðT 4 T 1 Þ
h Otto ¼ ¼ ¼ 1
Q 23 T 3 T 2 ðT 3 T 2 Þ (3.15)
heat rejected
¼ 1 :
heat added