- Why does the thermal efficiency depend only on the compression ratio and not on the amount of heat added?
- In the idealized Otto cycle, both the heat added (Q_in) and the heat rejected (Q_out) are proportional to the temperature change during their respective constant-volume processes. Their ratio, and thus the efficiency η = 1 − Q_out/Q_in, simplifies to an expression involving only the temperature ratio. For adiabatic processes, this temperature ratio is determined solely by the compression ratio and γ. Therefore, while adding more heat increases the net work (the cycle area), it does not change the fraction of heat input converted to work.
- How does the real-world gasoline engine differ from this ideal model?
- Real engines deviate significantly from the ideal Otto cycle. Combustion is not instantaneous or perfectly isochoric, there are substantial heat losses to the cylinder walls, the working fluid's composition and specific heats change during combustion, and friction and pumping losses occur. Furthermore, to prevent 'knocking,' real engines operate at compression ratios lower than the theoretical maximum. These factors mean the actual thermal efficiency is considerably lower than the ideal prediction.
- What is the physical significance of the heat capacity ratio (γ) in the efficiency equation?
- The heat capacity ratio, γ = Cp/Cv, is a property of the working fluid. A higher γ means the gas heats up more for a given amount of energy input at constant volume, leading to a higher pressure rise. During the adiabatic strokes, a higher γ causes a steeper PV curve, resulting in a larger temperature difference for the same compression ratio. This translates to more work output during expansion and higher theoretical cycle efficiency.
- Why are the compression and expansion strokes modeled as adiabatic?
- These strokes are modeled as adiabatic (no heat transfer) because they occur very rapidly in an engine—on the order of milliseconds. The timescale is so short that there is negligible time for significant heat transfer to or from the cylinder walls. This is a key simplification that allows the use of the relations PV^γ = constant and TV^(γ−1) = constant to describe these processes.