A gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of $700^{\circ }\text{C}$ and $27.0^{\circ }\text{C}$ . (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).

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.