The Mean Effective Pressure (MEP) of an Otto cycle is directly proportional to the pressure ratio.

Explanation:

1. Understanding the Otto Cycle:
The Otto cycle is a theoretical thermodynamic cycle that describes the operation of a spark-ignition internal combustion engine. It consists of four processes: intake, compression, combustion, and exhaust. The cycle is idealized and assumes certain conditions, such as constant specific heat and ideal gas behavior.

2. Mean Effective Pressure (MEP):
The Mean Effective Pressure (MEP) is a parameter that characterizes the performance of an engine. It represents the average pressure in the combustion chamber throughout the power stroke. MEP is a useful measure because it allows for comparisons between engines of different sizes and configurations.

3. Pressure Ratio:
The pressure ratio in an Otto cycle is the ratio of the maximum pressure (during combustion) to the minimum pressure (at the end of the exhaust stroke). It is a measure of the compression ratio of the engine and is denoted by the symbol "r". A higher pressure ratio indicates a higher compression ratio, which leads to more efficient combustion.

4. Relationship between MEP and Pressure Ratio:
The MEP of an Otto cycle is directly proportional to the pressure ratio. This means that as the pressure ratio increases, the MEP also increases, and vice versa. Mathematically, this relationship can be expressed as:

MEP ∝ pressure ratio

5. Explanation:
The reason for this relationship can be understood by considering the combustion process in the Otto cycle. During combustion, the fuel-air mixture is ignited by the spark plug, leading to a rapid increase in pressure and temperature. This high-pressure combustion pushes the piston downward, generating work. The amount of work produced depends on the pressure in the combustion chamber.

By increasing the pressure ratio, the compression ratio of the engine increases. This results in a higher maximum pressure during combustion. As a result, the average pressure throughout the power stroke (MEP) increases, leading to more work output. Therefore, the MEP is directly proportional to the pressure ratio.

Conclusion:
In conclusion, the Mean Effective Pressure (MEP) of an Otto cycle is directly proportional to the pressure ratio. Increasing the pressure ratio leads to a higher MEP, indicating better engine performance.