Short Answer:
The air-standard efficiency of the Otto cycle is the ratio of the work output of the cycle to the heat supplied during combustion, assuming air behaves as an ideal gas. It depends only on the compression ratio and the specific heat ratio (γ) of the working fluid. The efficiency increases with higher compression ratio. The formula is:
Here, is the compression ratio and is the ratio of specific heats (Cp/Cv).
In simple terms, when the compression ratio increases, the engine becomes more efficient because the air-fuel mixture burns more completely and produces more useful work.
Detailed Explanation :
Air-standard efficiency of the Otto cycle
The Otto cycle is a thermodynamic cycle used to describe the operation of a spark-ignition internal combustion engine, such as those found in petrol engines. The air-standard efficiency is a theoretical measure of how effectively the cycle converts the supplied heat energy into mechanical work, assuming that the working fluid is pure air following the ideal gas laws and that all processes are reversible.
The cycle consists of four main processes — two isentropic (reversible adiabatic) and two constant-volume (isochoric) processes. It is also known as the constant volume cycle because heat addition and rejection take place at constant volume.
- Processes of the Otto Cycle
The four processes of the Otto cycle are:
- Process 1–2: Isentropic Compression
- The air-fuel mixture is compressed inside the cylinder with no heat transfer to the surroundings.
- Pressure and temperature increase, and volume decreases.
- This process increases the energy of the air before combustion.
- Formula:
- Process 2–3: Constant Volume Heat Addition
- Combustion takes place rapidly at constant volume due to the spark ignition.
- Temperature and pressure rise sharply, increasing the internal energy of the air.
- Heat added:
- Process 3–4: Isentropic Expansion (Power Stroke)
- The high-pressure gas expands adiabatically, doing work on the piston.
- Pressure and temperature drop as the gas expands.
- Formula:
- Process 4–1: Constant Volume Heat Rejection
- The exhaust valve opens, and heat is rejected at constant volume.
- The pressure and temperature decrease, completing the cycle.
- Heat rejected:
- Derivation of Air-standard Efficiency
The air-standard efficiency (η) of the Otto cycle is the ratio of net work output to heat supplied:
Substituting the expressions for heat transfer:
From the isentropic relations:
Now, by substituting these relations:
This is the air-standard efficiency equation of the Otto cycle.
- Factors Affecting Air-standard Efficiency
- Compression Ratio (r):
- Defined as , the ratio of maximum to minimum volume in the cylinder.
- Higher compression ratio gives better efficiency because it leads to greater temperature rise and better fuel utilization.
- However, too high a compression ratio can cause knocking in petrol engines, limiting efficiency improvement.
- Specific Heat Ratio (γ):
- The ratio of specific heats depends on the gas used.
- Air has γ ≈ 1.4 at normal conditions.
- Higher γ means better efficiency because it represents a more “elastic” working fluid that stores less heat.
- Type of Fuel and Combustion:
- Although the air-standard efficiency assumes air as the working fluid, in real engines, the combustion of air-fuel mixture affects actual efficiency.
- Better combustion leads to performance closer to the theoretical value.
- Engine Design:
- Factors such as valve timing, spark plug position, and cooling rate influence how close actual efficiency gets to the air-standard value.
- Significance of Air-standard Efficiency
The air-standard efficiency provides a theoretical upper limit for the performance of a petrol engine. It helps engineers compare different engine designs based on compression ratio and understand how design improvements can enhance fuel economy and power output.
For example:
- A petrol engine with a compression ratio of 8:1 gives a theoretical efficiency of about 56%.
- Increasing the compression ratio to 10:1 raises efficiency to around 60%.
However, actual efficiencies are lower (25–35%) due to mechanical, heat, and frictional losses.
Conclusion
The air-standard efficiency of the Otto cycle defines the ideal performance of a spark-ignition engine, assuming perfect conditions and reversible processes. It depends only on the compression ratio and specific heat ratio of air. The formula,
shows that increasing the compression ratio increases the efficiency. Although real engines cannot reach this ideal efficiency due to losses, this equation helps in designing more efficient and powerful petrol engines. It serves as a fundamental principle for evaluating and improving engine performance.