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A gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of $700^\circ\textrm{C}$ and $27.0^\circ\textrm{C}$ . (a) What is the maximum efficiency of a heat engine operating between these temperatures? (b) Find the ratio of this efficiency to the Carnot efficiency of a standard nuclear reactor (found in Example 15.4).
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
  1. $0.692$
  2. $1.45$
Solution Video

OpenStax College Physics Solution, Chapter 15, Problem 29 (Problems & Exercises) (0:46)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The maximum efficiency called the carnot efficiency for heat engine operating between reservoirs at different temperatures is 1 minus the cold temperature divided by the hot temperature and expressed in Kelvin. So it’s 1 minus 27 degree Celsius plus 273.15 Kelvin divided by 700 degree Celsius converted to Kelvin which is 0.692. Now in example 15.4, we are told that the best efficiency of a nuclear power plant is 0.476 and so finding the ratio of these efficiencies as 0.69157 divided by 0.476 which is 1.45.