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The Carnot engine is the most efficient heat engine operating between two temperatures. It consists of four reversible steps: (1) isothermal expansion at $T_H$ — gas absorbs $Q_H$, (2) adiabatic expansion — gas cools from $T_H$ to $T_C$, (3) isothermal compression at $T_C$ — gas rejects $Q_C$, (4) adiabatic compression — gas returns from $T_C$ to $T_H$.

Carnot efficiency: $\eta_C = 1 - T_C/T_H$ (temperatures must be in Kelvin). This is the absolute upper limit — no real engine can exceed it between the same reservoirs. The efficiency depends only on the temperature ratio, not on the working substance or the design of the engine.

Key implications: $\eta = 100\%$ requires $T_C = 0$ K, which is unattainable (Third Law). For $T_H = 500$ K and $T_C = 300$ K, $\eta_C = 40\%$ — only 40% of absorbed heat converts to work. Real engines (Otto, Diesel, Rankine) achieve lower efficiencies due to irreversibilities like friction, turbulence, and finite-rate heat transfer.

Common JEE trap: using Celsius instead of Kelvin. A Carnot engine between 127 degrees C and 27 degrees C has $\eta = 1 - 300/400 = 25\%$, not $(127-27)/127 = 78.7\%$.