Endoreversible Heat Engine 2D — Power at Maximum Efficiency

Classical thermodynamics tells you the ceiling on efficiency — the reversible Carnot limit, η_C = 1 − T_c/T_h — but a Carnot-efficient engine also runs infinitely slowly and delivers zero power, because reaching that limit means the working fluid barely differs from the reservoirs, so almost no heat can flow through it in finite time. This 2D simulator builds a more honest model: a piston engine coupled to hot and cold reservoirs through finite thermal conductance, whose working fluid sits at its own temperatures T₁ and T₂ between the two reservoirs. Drag the operating-point slider (or the live curve) and the engine numerically searches for the power-maximizing partner temperature at every step, plotting the power-vs-temperature curve live and comparing your operating point against both the unreachable Carnot ceiling and the Curzon-Ahlborn-Novikov efficiency at maximum power, η* = 1 − √(T_c/T_h) — the number that actually predicts the efficiency of real turbines and engines far better than Carnot does.