OTTO CYCLE
By EngineerProf PH/Engr. Raymart Bonete
The Otto cycle is the ideal cycle for spark-ignition reciprocating engines. It is named after Nikolaus A. Otto, who built a
successful four-stroke engine in 1876 in Germany using the cycle proposed by Frenchman Beau de Rochas in 1862 .
The Ideal Otto Cycle: P-V and T-S Diagram
Process 3 → 4: Isentropic Expansion
𝑃𝑉 = 𝑚𝑅𝑇
P= Absolute Pressure=Patm+ Pgage
V= volume, m= mass
R= Gas Constant
T= Absolute Temperature (K;R)
𝑃3 𝑉3 𝑘 = 𝑃4 𝑉4 𝑘 ;
𝑇4
𝑉3 𝑘−1
=( )
𝑇3
𝑉4
𝑘𝐽
𝑐𝑝 = 1.0062
𝑐𝑣
𝑘𝑔𝑚 𝐾
= 0.24
𝐵𝑡𝑢
𝑙𝑏𝑚 𝑅
(ideal gas)
where k=1.4 which is the specific heat ratio at room air
temperature.
𝑐𝑣 =
𝑐𝑝
𝑘
𝑘−1
𝑘
Since 𝑣2 = 𝑣3 and 𝑣1 = 𝑣4 then;
𝑇1
𝑉2 𝑘−1
𝑉3 𝑘−1 𝑇4
=( )
=( )
=
𝑇2
𝑉1
𝑉4
𝑇3
; 𝑐𝑝 − 𝑐𝑣 = 𝑅 where R is the specific gas constant
(b) 𝑅 = 0.287
𝑅̅ = 8.314
𝑅=
𝑇4
𝑃4
=( )
𝑇3
𝑃3
Constants and Conversions
𝑐𝑝
(a) 𝑘 =
IDEAL GAS LAW
𝑘𝐽
𝑘𝑔𝑚 𝐾
𝑘𝐽
𝑘𝑚𝑜𝑙 𝐾
𝑓𝑡 𝑙𝑏𝑓
= 53.34 𝑙𝑏
𝑚𝑅
𝑓𝑡 𝑙𝑏𝑓
= 1545 𝑙𝑏𝑚𝑜𝑙 𝑅 (Universal Gas Constant)
𝑅̅
𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑔𝑎𝑠
Process 4 → 1: Constant Volume Heat Rejection
𝑣1 = 𝑣4
Heat Rejected; 𝑄𝑜𝑢𝑡 = 𝑚𝑐𝑣 (𝑇4 − 𝑇1) = 𝑚(𝑈4 − 𝑈1)
𝑃4 𝑃1
=
𝑇4 𝑇1
Temperature Conversions
℉ = 1.8℃ + 32 ; 𝐾 = ℃ + 273; 𝑅 = ℉ + 460
Pressure Conversions
1 atm (atmosphere) = 101.325 kPa
1 atm = 14.7 psi = 760 mm Hg = 760 Torr = 1.0332 kgf/cm 2
Mass Conversions
1 kgm = 2.2046 lbm
𝑇
𝑃1 𝑉1𝑘 = 𝑃2 𝑉2 𝑘 ; 𝑇1 =
2
𝑄𝑖𝑛 = 𝑚(𝑈3 − 𝑈2 )
;
𝑃2
𝑇2
=
𝑃3
𝑇3
𝑊𝑛𝑒𝑡 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡
𝑄𝑜𝑢𝑡
=
=1−
𝑄𝑖𝑛
𝑄𝑖𝑛
𝑄𝑖𝑛
𝑇4 − 𝑇1
𝑇3 − 𝑇2
1
= 1− 𝑘
𝑟𝑘 − 1
𝜂𝑡ℎ = 1 −
𝑣
𝑉
Where 𝑟𝑘 =compression ratio = 𝑣𝑚𝑎𝑥 = 𝑉1
𝑘−1
𝑃2 𝑘
= (𝑃 )
1
Process 2 → 3: Constant Volume Heat Addition
𝑣2 = 𝑣3
Heat Added: 𝑄𝑖𝑛 = 𝑚𝑐𝑣 (𝑇3 − 𝑇2 )
If Internal Energy is given by Air Tables:
𝜂𝑡ℎ =
𝜂𝑡ℎ
Process 1 → 2: Isentropic Compression
Isentropic Relations: PVk=Constant
𝑉 𝑘−1 𝑇
(𝑉2 ) ; 𝑇2
1
1
Thermal Efficiency
𝑚𝑖𝑛
Mean Effective Pressure (MEP)
Wnet = MEP X Piston Area X Stroke
Piston Area X Stroke= Volume Displacement (VD)
𝑣𝐷 = 𝑣𝑚𝑎𝑥 − 𝑣𝑚𝑖𝑛 = 𝑉1 − 𝑉2
Therefore; 𝑀𝐸𝑃 =
𝑊𝑛𝑒𝑡
𝑣𝐷
Reference: (Images) Thermodynamics: An Eng’g Approach by Cengel and Boles
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