ME 200 L35 Ground Transportation
(Air Standard Otto Cycle) 9.1 and 9.2
Kim See’s Office ME Gatewood Wing Room 2172
Examination and Quiz grades are available Blackboard
Examinations and Quizzes can be picked up all of this week from
Gatewood Room 2172
Material not picked up this week may be recycled!
https://engineering.purdue.edu/ME200/
ThermoMentor© Program
Spring 2014 MWF 1030-1120 AM
J. P. Gore
gore@purdue.edu
Gatewood Wing 3166, 765 494 0061
Office Hours: MWF 1130-1230
TAs: Robert Kapaku rkapaku@purdue.edu
Dong Han han193@purdue.edu
Introducing Engine Terminology
► Displacement volume: volume
swept by piston when it moves from
top dead center to bottom dead
center
Top dead center
Stroke
Bottom dead center
►Compression ratio, r : volume
at bottom dead center divided by
volume at top dead center
Air-Standard Otto Cycle
►The Otto cycle consists of four internally reversible
processes in series:
►Process 1-2: isentropic compression.
►Process 2-3: constant-volume heat addition to the air
from an external source.
►Process 3-4: isentropic expansion.
►Process 4-1: constant-volume heat transfer from the
air.
►The Otto cycle
compression ratio is:
V1 V4
r

V2 V3
Air-Standard Otto Cycle:
r is important!
V1 V4 v1 v4
r   
V2 V3 v2 v3
(1) Define Compression Ratio
p1V1 p2V2 rp1V2
p2
T2



r
T1
T2
T1
p1
T1
(2) Ideal Gas Law and eq. (1)
k
p2  V1 
p V  p2V2 
    rk
p1  V2 
p2
T2
T2
T2
k
 r  r  r   r k 1
p1
T1
T1
T1
k
1 1
k
(3) Isentropic compression
(4) Combine (2) & (3)
T2
k 1 p2
k v2
1
r ;
r ; r
T1
p1
v1 Compression Ratio is
Very IMPORTANT!
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Air-Standard Otto Cycle
►Ignoring kinetic and potential energy effects, closed system
energy balances for the four processes of the Otto cycle reduce to
give
w12  u2  u1 , w34  u3  u4 , q23  u3  u2 , q41  u4  u1
►The thermal efficiency is the ratio of the net work to the heat
added and for air standard cycle with constant specific heats,
it reduces to solely a function of compression ratio::
W12  W34 (u2  u1 )  (u3  u4 )
Th 

Q23
u3  u2
Q23  Q41  u3  u2   (u4  u1 )
(T  T )


 1 4 1
Q23
 u3  u2 
T3  T2 
T
 1 1
T2
 T / T   1  1  T
T
 T / T   1
4
3
1
2
1
2
 1
1
r k 1
Compression Ratio is
Very IMPORTANT!
►Consider an Otto cycle with a compression ratio of 8.5 with constant specific
heats, specific heats as a function of temperature, and compression and
expansion with pv1.2 = constant instead of the isentropic process. Find: (i) heat
added, (ii) heat rejected, (iii) work done in the compression and expansion
strokes, (iv) thermal efficiency, and (v) break mean effective pressure.
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Air-Standard Otto Cycle
►Since the air-standard Otto cycle is composed of
internally reversible processes, areas on the T-s and
p-v diagrams can be interpreted as heat and work,
respectively:
►On the T-s diagram, heat transfer per unit of
mass is ∫Tds. Thus,
• Area 2-3-a-b-2 represents
heat added per unit of mass.
• Area 1-4-a-b-1 is the heat
rejected per unit of mass.
• The enclosed area is the net
heat added, which equals the
net work output.
Air-Standard Otto Cycle
►On the p-v diagram, work per unit of mass is
∫pdv. Thus,
• Area 1-2-a-b-1 represents
work input per unit of mass
during the compression
process.
• Area 3-4-b-a-3 is the work
done per unit of mass in the
expansion process.
• The enclosed area is the net
work output, which equals the
net heat added.
Air-Standard Otto Cycle
►The compression ratio, r = V2/V1, is an important
operating parameter for reciprocating internal combustion
engines as brought out by the following discussion
centering on the T-s diagram:
►An increase in the compression ratio
changes the cycle from 1-2-3-4-1 to
1-2′-3′-4-1.
►Since the average temperature of heat
addition is greater in cycle 1-2′-3′-4-1,
and both cycles have the same heat
rejection process, cycle 1-2′-3′-4-1 has
the greater thermal efficiency.
►Accordingly, the Otto cycle thermal
efficiency increases as the
compression ratio increases.
►Now consider an Otto cycle with a compression ratio of 12.5 with (a) constant
specific heats, (b) specific heats as a function of temperature, and (c)
compression and expansion with pv1.2 = constant instead of the isentropic
process. Find: (i) heat added (kJ/kg), (ii) heat rejected (kJ/kg), (iii) work done in
the compression (kJ/kg) and expansion strokes (kJ/kg), (iv) thermal efficiency,
and (v) break mean effective pressure.
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►Consider an Otto cycle with a compression ratio of 8.5 with constant specific
heats, specific heats as a function of temperature, and compression and
expansion with pv1.2 = constant instead of the isentropic processes.
Considering internal irreversibilities only, find: (I) Entropy change and (II)
Entropy generation during each of the processes: 1-2, 2-3, 3-4, and 4-1.
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