| State | P (kPa) | V (L) | T (K) |
|---|
Every point on a PV diagram is a state of the gas — a pressure and volume (and, via the ideal gas law, a temperature). Move along a curve and the gas does work, W = ∫P dV — literally the area under that segment. A full cycle traces a closed loop, and the net work output is the area enclosed by the loop: clockwise means net work is done by the gas — an engine. This tool solves every state point exactly from the ideal gas law and each process's own equation (isochoric, isobaric, isothermal, or adiabatic), then integrates for work and heat directly — nothing here is a canned efficiency number, it's computed state by state and cross-checked against the standard closed-form efficiency formula for each cycle.
An Otto cycle (petrol engine) at a compression ratio of 8:1 — typical for a road-car engine — has an ideal air-standard efficiency of 56.5%, from the closed form η = 1 − r^(1−γ). Real engines manage roughly half that once friction, heat loss and real combustion are accounted for — the ideal cycle is a ceiling, not a prediction.
Diesel engines run much higher compression ratios in practice (16–22:1 vs. roughly 8–12:1 for petrol) precisely because they inject fuel only at the top of the stroke, avoiding the pre-ignition ("knock") that limits how far a petrol/air mixture can be compressed — the higher ratio, not the cycle shape itself, is what usually gives Diesel engines their efficiency edge in practice.
Carnot's cycle is built entirely from reversible isothermal and adiabatic steps, and for those the Second Law fixes the efficiency purely by the hot and cold reservoir temperatures — it's the theoretical ceiling no real heat engine operating between those two temperatures can exceed, regardless of working fluid or mechanism.
Gas turbines and jet engines — continuous-flow compression, combustion and expansion rather than a piston's stop-start strokes, which is exactly why its efficiency depends on pressure ratio instead of the volumetric compression ratio the piston cycles use.
Real gases aren't ideal, combustion isn't instantaneous heat addition, compression and expansion aren't frictionless or adiabatic, and every real cycle loses heat through the cylinder walls — each of these gaps costs real efficiency the air-standard analysis can't see.