The performance of any heat engine can be mapped out as a thermodynamic cycle. These cycles, often plotted on pressure-volume (P-V) or temperature-entropy (T-S) diagrams, show us how an engine's working fluid changes state to produce work. For internal combustion engines, the two most important ideal cycles are the Otto and Diesel cycles.

Both cycles model the four-stroke process: intake, compression, power (combustion), and exhaust. However, they differ in a crucial step: how heat is added. The Otto cycle assumes instantaneous combustion, adding heat at a constant volume. This is a decent model for a spark-ignition petrol engine. The Diesel cycle, on the other hand, assumes heat is added at a constant pressure, which better reflects the slower fuel injection and combustion process in a compression-ignition diesel engine.

This difference in heat addition directly impacts thermal efficiency. The ideal efficiency for an Otto cycle depends only on the compression ratio ($r$) and the specific heat ratio ($\gamma$).

For a Diesel cycle, the equation is a bit more complex. It also depends on the cut-off ratio, $r_c$, which is the ratio of the volume after combustion to the volume before combustion.

External combustion engines, like those in power plants, operate differently. The fuel is burned outside the engine to heat a separate working fluid, typically water, which then turns into steam. The ideal cycle for these systems is the Rankine cycle., which describes the process of a steam turbine.

The key advantage here is fuel flexibility. Because combustion is external, you can use a wide variety of heat sources, from coal and natural gas to nuclear fission or concentrated solar power. This makes the Rankine cycle ideal for large-scale, stationary power generation. However, the need for boilers, condensers, and pumps makes these systems large, heavy, and slow to start up, which is why they aren't used in cars.

Internal combustion engines dominate mobile applications because of their high power-to-weight ratio and rapid response. External combustion engines excel in stationary applications where high overall efficiency and fuel flexibility are more important than size or weight.

Ultimately, the choice of cycle is a game of trade-offs driven by the application. An internal combustion engine is designed for scenarios where quick, on-demand power in a compact package is essential. The working fluid (the air-fuel mixture) is used once and then expelled. In a Rankine cycle, the working fluid (water) is continuously recycled in a closed loop, which allows for much greater control over the thermodynamic process to maximize efficiency, but at the cost of complexity and size.

This highlights the core difference. The design of a car engine is constrained by mechanics, weight, and cost. The design of a power plant turbine is governed almost purely by the quest for maximum thermal efficiency from a given heat source.

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