Thermodynamics

The Otto and Diesel Cycles: Gasoline and Diesel Engines

Gas cycles, no phase change. Otto burns at constant V, Diesel at constant P. η = 1 − 1/r^γ−1; diesel wins with a higher r

The engine under most cars' hoods runs not on a phase change but on air alone, heated by burning fuel inside the cylinder. The Otto and Diesel cycles share four strokes and differ in one thing: whether the fuel burns at constant volume or constant pressure.

Drag the phase to follow the Otto cycle. Compress the air adiabatically, add heat at constant volume when the spark fires, expand for the power stroke, then dump heat at constant volume. In a real four-stroke engine only the expansion stroke delivers power, and the flywheel's stored inertia carries the piston through the other three.

The ideal Otto efficiency depends only on the compression ratio: η = 1 − 1r^γ−1. Squeeze the charge into a smaller fraction of the cylinder and efficiency climbs. The gain per extra unit of r shrinks as r rises, though, so at very high compression ratios the efficiency curve flattens out. Drag r.

The two cycles differ in the combustion leg. Otto burns at constant volume -- a spark, a vertical jump on P-V. Diesel burns at constant pressure -- fuel injected as the piston moves, a horizontal step. The spark burns the premixed charge in a flash, leaving the piston no time to move so the volume barely changes, while the diesel sprays fuel in gradually and the burning keeps pace with the descending piston, holding the pressure nearly constant. Toggle them.

A gasoline engine compresses fuel and air together, so knock caps its compression ratio. A diesel compresses air alone and injects fuel only at the top, so it can run a much higher ratio -- and reach higher efficiency. That is why diesels power most trucks, ships, and heavy machinery, where fuel economy rules, while the lighter, higher-revving gasoline engine suits passenger cars. Toggle gasoline and diesel.

Three takeaways: both are gas cycles with no phase change, they differ only in constant-V vs constant-P combustion, and the compression ratio is the master knob. Next, run a cycle backward to move heat uphill: refrigeration. Real engines actually burn in a blend of the two, part at constant volume and part at constant pressure, a mix known as the dual cycle.

In PracticeTo sum up: Otto and Diesel are internal-combustion cycles that use air with no phase change. They share four strokes (adiabatic compression, combustion, adiabatic expansion, constant-volume exhaust), but Otto adds heat at constant volume (spark ignition) and Diesel at constant pressure (compression ignition). The ideal Otto efficiency η = 1 − 1r^γ−1 is fixed by the compression ratio r alone and rises with r. Gasoline compresses fuel too, so knock limits its r; a diesel compresses air alone and can run a much higher r, so it is more efficient in practice. At the same r a diesel is slightly below Otto because of its cutoff (injection) leg, but its higher r more than reverses that. Next, D3 runs these cycles backward as refrigerators and heat pumps, spending work to lift heat from cold to hot.

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