Explanation:

The Otto cycle and Diesel cycle are two ideal thermodynamic cycles that are commonly used in internal combustion engines. Both cycles involve four processes: intake, compression, combustion, and exhaust. However, the main difference between them is the way in which the fuel is ignited.

- Otto Cycle: In the Otto cycle, the fuel-air mixture is ignited by a spark plug. This causes an explosion in the combustion chamber, which pushes the piston down and generates power.

- Diesel Cycle: In the Diesel cycle, the fuel is injected into the combustion chamber at high pressure and temperature, causing it to ignite spontaneously. This creates a controlled explosion that generates power.

Efficiency Comparison:

- Compression Ratio: The compression ratio is the ratio of the maximum volume of the combustion chamber to the minimum volume. Both the Otto cycle and Diesel cycle have the same compression ratio for the same engine.

- Heat Input: The heat input is the amount of heat energy added to the system during combustion. Both cycles have the same heat input for the same engine.

- Efficiency: The efficiency of a cycle is the ratio of the net work output to the heat input. The Otto cycle has a higher efficiency than the Diesel cycle for the same compression ratio and heat input.

Reason:

The reason for this is that the Otto cycle has a higher maximum temperature and lower heat rejection than the Diesel cycle.

- Maximum Temperature: The maximum temperature is the highest temperature reached during combustion. In the Otto cycle, the fuel-air mixture is ignited by a spark plug, which creates a controlled explosion. This explosion generates a high temperature, which results in a high thermal efficiency. In the Diesel cycle, the fuel is injected into the combustion chamber at high pressure and temperature, causing it to ignite spontaneously. This creates a less controlled explosion, which results in a lower maximum temperature and lower thermal efficiency.

- Heat Rejection: The heat rejection is the amount of heat energy that is not converted into work and is lost to the environment. In the Otto cycle, the combustion occurs at constant volume, which means that there is no heat rejection during combustion. In the Diesel cycle, the combustion occurs at constant pressure, which means that there is some heat rejection during combustion. This results in a higher heat rejection and lower thermal efficiency in the Diesel cycle.

Conclusion:

Therefore, the Otto cycle has a higher efficiency than the Diesel cycle for the same compression ratio and heat input because of the higher maximum temperature and lower heat rejection.