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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 the reservoirs at different temperatures is one minus the cold temperature and divided by the hot temperature and expressed in Kelvin. So it’s one 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 ratios of these efficiencies as 0.69157 divided by 0.476 which is 1.45.