Question
Would you be willing to financially back an inventor who is marketing a device that she claims has 25 kJ of heat transfer at 600 K, has heat transfer to the environment at 300 K, and does 12 kJ of work? Explain your answer.
Final Answer
No, I would not support this inventor. The claimed efficiency is 96% of the maximum possible efficiency. Real engines can't do better than 70% of the Carnot efficiency.
Solution video
OpenStax College Physics for AP® Courses, Chapter 15, Problem 34 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. This inventor has created an engine that does 12 kilojoules of work operating between reservoirs with a high temperature of 600 Kelvin and 300 Kelvin and it absorbs 25 kilojoules of heat. So the efficiency then is the work done divided by the heat absorbed and so that's 12 kilojoules divided by 25 kilojoules which is an efficiency of 48 percent. But we know that the maximum possible efficiency is the Carnot efficiency which is 1 minus the cold temperature reservoir divided by the hot temperature reservoir so that's 1 minus 300 Kelvin divided by 600 Kelvin which is 50 percent. So no I would not support this investor because the claimed efficiency of 48 percent is 96 percent of the maximum possible efficiency and real engines can't normally do better than 70 percent of the Carnot efficiency.