Modern Engineering Thermodynamics

13.18 Otto Cycle 505
Exercises
40. If the lawn mower in Example 13.14 is left outside on a cold day when T 3 is reduced from 70.0°F to 30.0°F, determine
the new temperature at the end of the isentropic compression stroke. Assume all the other variables remain unchanged.
Answer: T 4s = 1130 R.
41. If the clearance volume on the lawn mower in Example 13.14 is decreased such that the compression ratio is increased
from 8.00 to 8.50 to 1, determine the new pressure at the end of the isentropic compression stroke. Assume all the other
variables remain unchanged. Answer: p 4s = 294.1 psia.
42. If the maximum temperature in the cycle (T 4s ) is 2400 R, determine the Otto cycle hot ASC thermal efficiency of this
engine. Assume all the other variables remain unchanged. Answer: (η T ) Otto hot ASC = 52.8%.
The actual pressure–volume diagram from an engine operating on a gas or vapor power cycle is called an indicator
diagram, 10 and the enclosed area is equal to the net reversible work produced inside the engine. The mean effective
pressure (mep) of a reciprocating engine is the average net pressure acting on the piston during its displacement. The
indicated (or reversible) work output ðW I Þ out of the piston is the net positive area enclosed by the indicator diagram,
as shown
in Figure 13.49, and is equal to the product of the mep and the piston displacement,
V 2 − V 1 = π 4 ðBoreÞ 2 ðStrokeÞ, or
ðW I Þ out
= mep ðV 2 − V 1 Þ (13.31)
The indicated power output ð _W I Þ out is the net (reversible) power developed inside all the combustion chambers
of an engine containing n cylinders and is
ð _W I Þ out = mepðnÞðV 2 − V 1 ÞðN/CÞ (13.32)
where N is the rotational speed of the engine and C is the number of crankshaft revolutions per power stroke
(C = 1 for a two-stroke cycle and C = 2 for a four-stroke cycle). The actual power output of the engine as measured
by a dynamometer is called the brake power ð _W B Þ out, and the difference between the indicated and brake
power is known as the friction power (i.e., the power dissipated in the internal friction of the engine) _W F ,or
ð _W I Þ out = ð _W B Þ out + _W F
therefore, the engine’s mechanical efficiency η m is simply (see Table 13.2)
From Eq. (13.31), we can write
η m =
_W actual
_W reversible
= ð _W B Þ out
ð _W I Þ out
= 1 −
_W F
ð _W I Þ out
(13.33)
mep = ðW I Þ out
/ðV 2 − V 1 Þ = ðW I Þ out
/m a /v2 − v 1
= ð _W I Þ out / _m a / ð v2 − v 1 Þ
Area = Expansion work
Area = (W I ) out
p
Area = Suction
work (intake)
mep + p atm
p
p atm
mep
V 1 V 2 V 1 V 2
V
V
(W I ) out = Expansion work p−V area
(W I ) out = (mep)(V 2 − V 1 )
− Suction work p−V area
(a) Actual indicator diagram
(b) Equivalent mep diagram
FIGURE 13.49
Mean effective pressure (mep) and indicator diagram relation.
10 The term indicator diagram dates from about 1790, when James Watt developed an apparatus to continuously record (i.e., indicate)
the variations in pressure within a steam engine cylinder. It is used today to denote any p−V diagram that is constructed from actual
pressure–volume data.