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A coal-fired electrical power station has an efficiency of 38%. The temperature of the steam leaving the boiler is $550^\circ\textrm{C}$. What percentage of the maximum efficiency does this station obtain? (Assume the temperature of the environment is $20^\circ\textrm{C}$.)
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Final Answer

59% of maximum efficiency.

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OpenStax College Physics Solution, Chapter 15, Problem 33 (Problems & Exercises) (1:10)

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This is College Physics Answers with Shaun Dychko. A coal-fired electric power plant has an efficiency of 38 percent which is 0.38 and has a steam temperature of 550 degrees Celsius, that'll be <i>Th</i> for the temperature of the hot reservoir. And then, the cold reservoir is the environment into which some of the waste heat is expelled and that's at 20 degrees Celsius. So, the maximum possible efficiency is the Carnot efficiency and we're going to take a ratio of the actual efficiency divided by the Carnot efficiency. And so, the Carnot efficiency is one minus cold temperature divided by the hot temperature. So, that's one minus 20 degrees Celsius converted into Kelvin by adding 273.15 divided by 550 degrees Celsius converted into Kelvin, and this works out to 0.64387. That's the maximum theoretical efficiency. And so, the actual efficiency divided by the Carnot efficiency 0.38 divided by 0.64387 which 0.59. And so, it's operating at 59 percent of its maximum possible efficiency.