Carnot Efficiency

No matter how brilliant the engineering, a heat engine operating between steam at 600 degrees C and cooling water at 30 degrees C cannot convert more than 65% of its heat input to work. This ceiling is not a technology limitation. It is a consequence of the second law of thermodynamics, derived by Sadi Carnot in 1824.

Coal steam at 600°C and cooling water at 30°C sets a Carnot ceiling near 65%; gas turbine combustion at 1,400°C pushes that ceiling to 82%. Both numbers come from the same formula: eta_Carnot = 1 - T_cold/T_hot, in Kelvin (K = degrees C + 273), a consequence of the second law derived by Sadi Carnot in 1824. Two levers exist for improvement: raise T_hot (why materials science matters for turbine blades) or lower T_cold (limited in practice by ambient temperature). Real plants land at 50-80% of their Carnot ceiling: 38-45% for coal, 38-42% for simple-cycle gas.

Why does the gas turbine achieve roughly the same actual efficiency as the coal plant despite a much higher Carnot ceiling?

The compressor penalty. The gas turbine's compressor consumes 50-60% of gross output (compressing gas is energy-intensive). This large internal load pulls actual efficiency far below the Carnot ceiling. Combined-cycle plants recover exhaust heat to close more of the gap, reaching 55-63%.

Carnot efficiency explains why materials research, combined cycles, and cooling water access directly determine power plant economics.

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