Carnot Engine

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Operating between a boiler at 600 K and a condenser at 300 K, an ideal reversible engine runs through a complete Carnot cycle. What is the maximum possible efficiency it can achieve?

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A Carnot engine sets the upper limit on efficiency for any engine running between two fixed temperatures, given by $\eta_{	ext{Carnot}} = 1 - \dfrac{T_C}{T_H}$ with temperatures in kelvin. Substituting $T_C = 300	ext{ K}$ and $T_H = 600	ext{ K}$ gives $\eta = 1 - 300/600 = 1 - 0.5 = 0.5$, or 50 percent. The value 100 percent is impossible because it would require a cold reservoir at absolute zero, forbidden by the Second Law. The value 67 percent likely comes from using a wrong temperature ratio such as $1 - 200/600$. The value 33 percent inverts the ratio to $T_H/T_C$ incorrectly. The Carnot formula uses absolute temperature because efficiency derives from the ratio of heat exchanged, which scales with kelvin. No real engine operating between the same two reservoirs can exceed this Carnot value, since any greater efficiency would let a composite device violate the Second Law by transferring heat from cold to hot with no work input. The result is also independent of the working substance, depending only on the two reservoir temperatures. As a consistency check, halving the absolute temperature across the cycle should waste half the input heat, leaving exactly half available as work, which matches the 50 percent result.

Carnot Engine

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