Page 65 - Entrophy Analysis in Thermal Engineering Systems

Most efficient engine 57

(5.3)
PR ¼ p max =p min
Indeed, CR denotes the maximum degree of volume change experienced by
the working gas, whereas PR is the highest degree of the pressure change
that the gaseous medium undergoes in each cyclical operation.

5.2.1 Stirling cycle
A p-V diagram of the Stirling cycle is depicted in Fig. 5.1. It consists of four
processes: isothermal compression with heat removal 1!2, isochoric heat
addition 2!3, isothermal expansion with heat addition 3!4, and
isochoric heat removal 4!1. Thus, we have T 1 ¼T 2 , V 2 ¼V 3 , T 3 ¼T 4 ,
and V 4 ¼V 1 . The thermal efficiency of the Stirling cycle is the same as
the Carnot efficiency. Hence,

T 1
η ¼ 1 (5.4)
T 3
Using the relation p 1 V 1 /T 1 ¼p 3 V 3 /T 3 , Eq. (5.4) can be expressed as

p 1 V 1
η ¼ 1 (5.5)
p 3 V 3
The compression and pressure ratios for the Stirling cycle are CR¼V 1 /V 3
and PR¼p 3 /p 1 . Eq. (5.5) may now be represented in terms of CR and PR.

CR
η ¼ 1 (5.6)
PR

Fig. 5.1 A p-V diagram of the Stirling cycle.