Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

502 | Thermodynamics

the end of each process, (b) the net work output and the thermal efficiency,

and (c) the mean effective pressure.

Solution An ideal Diesel cycle is considered. The temperature and pressure

at the end of each process, the net work output, the thermal efficiency, and

the mean effective pressure are to be determined.

Assumptions 1 The cold-air-standard assumptions are applicable and thus

air can be assumed to have constant specific heats at room temperature.

2 Kinetic and potential energy changes are negligible.

Properties The gas constant of air is R
0.3704 psia · ft^3 /lbm · R and its

other properties at room temperature are cp
0.240 Btu/lbm · R, cv


0.171 Btu/lbm · R, and k
1.4 (Table A–2Ea).

Analysis The P-Vdiagram of the ideal Diesel cycle described is shown in

Fig. 9–24. We note that the air contained in the cylinder forms a closed

system.

(a) The temperature and pressure values at the end of each process can be

determined by utilizing the ideal-gas isentropic relations for processes 1-2

and 3-4. But first we determine the volumes at the end of each process from

the definitions of the compression ratio and the cutoff ratio:

Process 1-2 (isentropic compression of an ideal gas, constant specific heats):

Process 2-3 (constant-pressure heat addition to an ideal gas):

Process 3-4 (isentropic expansion of an ideal gas, constant specific heats):

(b) The net work for a cycle is equivalent to the net heat transfer. But first

we find the mass of air:

m

P 1 V 1

RT 1

1 14.7 psia 21 117 in^32

1 0.3704 psia#ft^3 >lbm#R 21 540 R 2

a

1 ft^3

1728 in^3

b
0.00498 lbm

P 4 
P 3 a

V 3

V 4

b

k


 1 841 psia2a

13 in^3

117 in^3

b

1.4


38.8 psia

T 4 
T 3 a

V 3

V 4

b

k 1


 1 3432 R2a

13 in^3

117 in^3

b

1.4 1


1425 R

P 2 V 2

T 2

P 3 V 3

T 3

ST 3 
T 2 a

V 3

V 2

b
 1 1716 R 2122 
3432 R

P 3 
P 2 
841 psia

P 2 
P 1 a

V 1

V 2

b

k


 1 14.7 psia 21182 1.4
841 psia

T 2 
T 1 a

V 1

V 2

b

k 1


 1 540 R 21182 1.4^1 
1716 R

V 4 
V 1 
117 in^3

V 3 
rcV 2 
 1221 6.5 in^32 
13 in^3

V 2 

V 1

r

117 in^3

18

6.5 in^3

1

(^23)
4
P, psia
Isentropic
Isentropic
14.7
V 2 = V 1 /18 V 3 = 2V 2 V 1 = V 4 V
qin
qout
FIGURE 9–24
P-Vdiagram for the ideal Diesel cycle
discussed in Example 9–3.