Question
What is wrong with the claim that a cyclical heat engine does 4.00 kJ of work on an input of 24.0 kJ of heat transfer while 16.0 kJ of heat transfers to the environment?
Final Answer
The difference between the heat input and output isn't equal to the work done. Therefore, this is not a cyclical engine, or the values given are wrong.
Solution video
OpenStax College Physics, Chapter 15, Problem 16 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A hypothetical cyclical engine does 4.00 kilojoules of work absorbing 24.0 kilojoules of heat and expelling 16.0 kilojoules of heat to the environment. So Q c to the cold reservoir is 16.0 and Q absorbed from the hot reservoir is 24.0. Now for cyclical engine, the work done is the difference between the heat absorbed and the heat expelled. So that's 24.0 minus 16.0 which is 8.0 kilojoules. However this 8.0 kilojoules does not equal the 4.00 kilojoules claimed for the work done and so the work done is not equal to Q h minus Q c. So that means this is either not a cyclical heat engine or there's something wrong with one of these numbers.