In terms of efficiency, what role does the compression ratio play in an Otto cycle?

The compression ratio in an Otto cycle is defined as the ratio of the maximum volume of the combustion chamber to the minimum volume. It plays a crucial role in determining the efficiency of the cycle. As the compression ratio increases, the efficiency of the Otto cycle also increases. This is because a higher compression ratio results in a more complete combustion of the fuel-air mixture, allowing for a greater expansion of gases and consequently more work output from the cycle.

Higher compression ratios lead to elevated temperatures and pressures in the combustion chamber, which improves the thermal efficiency according to the principles of thermodynamics. The efficiency of an ideal Otto cycle is given by the equation:

[ \eta = 1 - \frac{1}{r^{\gamma - 1}} ]

where ( r ) is the compression ratio and ( \gamma ) is the specific heat ratio (Cp/Cv). As ( r ) increases, the term ( \frac{1}{r^{\gamma - 1}} ) decreases, resulting in a higher overall efficiency ( \eta ).

This relationship emphasizes that an increase in the compression ratio enhances the thermal efficiency of the Otto cycle, making it a fundamental parameter in engine design to maximize efficiency.