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

Chapter 9 | 499

(b) The net work output for the cycle is determined either by finding the
boundary (PdV) work involved in each process by integration and adding
them or by finding the net heat transfer that is equivalent to the net work
done during the cycle. We take the latter approach. However, first we need
to find the internal energy of the air at state 4:
Process 3-4 (isentropic expansion of an ideal gas):

Process 4-1 (constant-volume heat rejection):

Thus,

(c) The thermal efficiency of the cycle is determined from its definition:

Under the cold-air-standard assumptions (constant specific heat values at
room temperature), the thermal efficiency would be (Eq. 9–8)

which is considerably different from the value obtained above. Therefore,
care should be exercised in utilizing the cold-air-standard assumptions.

(d) The mean effective pressure is determined from its definition, Eq. 9–4:

where

Thus,

Discussion Note that a constant pressure of 574 kPa during the power
stroke would produce the same net work output as the entire cycle.

MEP

418.17 kJ>kg

1 0.832 m^3 >kg 211 ^182

a

1 kPa#m^3

1 kJ

b
574 kPa

v 1 

RT 1

P 1

1 0.287 kPa#m^3 >kg#K 21 290 K 2

100 kPa

0.832 m^3 >kg

MEP

wnet

v 1 v 2

wnet

v 1 v 1 >r

wnet

v 111  1 >r 2

hth,Otto
 1 

1

rk^1

 1 r^1 k
 1  1821 1.4
0.565 or 56.5%

hth

wnet

qin

418.17 kJ>kg

800 kJ>kg

0.523 or 52.3%

wnet
qnet
qinqout
 800 381.83
418.17 kJ/kg

qout
588.74206.91
381.83 kJ>kg

qout
u 1 u 4 S qout
u 4 u 1

u 4 
588.74 kJ>kg

vr 4

vr 3

v 4

v 3

r S vr 4 
rvr 3 
 1821 6.108 2 
48.864ST 4 
795.6 K

 1 1.7997 MPa2a

1575.1 K

652.4 K

b1 12 
4.345 MPa

P 3 v 3

T 3

P 2 v 2

T 2

S P 3 
P 2 a

T 3

T 2

ba

v 2

v 3

b