Heat flows from a reservoir at $$373$$ K to a reservoir at $$273k$$ through a copper rod as shown in the figure. The heat then leaves the $$273K$$ reservoir and enters a Carnot engine, which uses part of this heat to do work and rejects the remainder to a third reservoir at $$173K$$.What fraction of the heat leaving the $$373K$$ reservoir is rendered unavailable for doing work, as compared to the situation where a Carnot engine is connected directly between the $$373K$$ and $$173K$$ reservoirs?

Question

Infinity Learn · Accepted Answer

[Concept]: With reservoirs at $$273K$$,$$173K$$[Step $$1$$]: $$WQ=273$$−$$173273=0.37$$  [Concept]: With reservoirs at $$373K$$, $$173K$$[Step $$2$$]:   $$WQ=373$$−$$173373=0.54$$[Step $$3$$]:   W'−$$W=0.54$$−$$0.37Q=0.17Q$$​⇒W'−$$WQ=0.17$$​⇒W'−$$WQ100=0.17$$×$$100=17$$%

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