In my previous article, I gave a short introduction to Otto cycle and discussed the processes in it. In this article, I will derive the airstandard efficiency of Otto cycle.
pV and Ts Diagrams of Otto Cycle:
pV Diagram  Ts Diagram 

Basic terms used in derivation of airstandard efficiency of Otto cycle:
Total Cylinder Volume:
It is the total volume (maximum volume) of the cylinder in which Otto cycle takes place. In Otto cycle,
Total cylinder volume = V_{1} = V_{4} = V_{c} + V_{s} (Refer pV diagram above)
where,
V_{c} → Clearance Volume
V_{s} → Stroke Volume
Clearance Volume (V_{c}):
At the end of the compression stroke, the piston approaches the Top Dead Center (TDC) position. The minimum volume of the space inside the cylinder, at the end of the compression stroke, is called clearance volume (V_{c}). In Otto cycle,
Clearance Volume, V_{c} = V_{2} (See pV diagram above)
Stroke Volume (V_{s}):
In Otto cycle, stroke volume is the difference between total cylinder volume and clearance volume.
Stroke Volume, V_{s} = Total Cylinder Volume – Clearance Volume = V_{1} – V_{2} = V_{4} – V_{3}
Compression Ratio:
Compression ratio (r) is the ratio of total cylinder volume to the clearance volume.
Now that we know the basic terms, let us derive expressions for T_{2} and T_{3}. These expressions will be useful for us to derive the expression for airstandard efficiency of otto cycle. For finding T_{2}, we take process 12 and for finding T_{3}, we take process 34.
Process 12:
This process is an isentropic (reversible adiabatic) process. For this process, the relation between T and V is as follows:
Process 34:
This is also an isentropic process. The relation between T and V in this process is similar to the relation between T and V in process 12:
Here,
Airstandard efficiency of Otto cycle:
It is defined as the ratio between work done during Otto cycle to the heat supplied during Otto cycle.
AirStandard Efficiency (thermal efficiency) of Otto cycle,
From my previous article,
If you have any ideas or suggestions about airstandard efficiency of Otto cycle, you can comment on this article.
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