76
2 Macroscopic Thermodynamics
Similarly, the heat (energy) export occurs during the final, isochoric, step: as
W rev
4→1 (fluid) ≡ 0 for an isochoric process, Q export ≡ −Q rev
4→1 (fluid). Moreover,
Q rev
4→1 (fluid) is given by
Q
rev
4→1 (fluid) = ((U ) 4→1
= C V (T min − T low ) < 0 ,
since T min < T low . Thus, we see that
Q export = C V (T low − T min ) .
(2.5.46b)
The efficiency for the Diesel cycle is thus
η Diesel = 1 −
Q export
Q import
= 1 −
C V (T low − T min )
C P (T max − T high )
or
η Diesel = 1 −
T low − T min
γ (T max − T high )
.
(2.5.47)
It is traditional to express the efficiency for the Diesel cycle in terms of pressure and
volume as
η Diesel = 1 −
1
γ
P 4 V 4 − P 1 V 1
P 3 V 3 − P 2 V 2
or, since V 4 = V 1 and P 3 = P 2 for a Diesel engine, as
η Diesel = 1 −
P 1 V 1
γ P 2 V 2
P 4
P 1
− 1
V 3
V 2
− 1
.
From Fig. 2.4b, the trapezoidal geometry of the Diesel cycle gives the slope of the
adiabatic power cycle path (3 → 4) as
ln P 4 − ln P 1
ln V 2 − ln V 3
= −γ , or
P 4
P 1
=
V 3
V 2
γ
,
(2.5.48a)
while the initial adiabatic compression from (V 1 , P 1 ) to (V 2 , P 2 ) similarly gives