Question #302347

01)  An inventor claims to have developed a heat engine that receives 700Kj of heat from a source at 500K and produces 300Kj of net work while rejecting the waste heat to a sink at 290K. is this reasonable claim?



1
Expert's answer
2022-02-25T12:37:01-0500

The maximum heat efficiency of the engine is the Carnot efficiency;

ηCarnot=1T2T1=1290500=0.42\eta_{Carnot}=1-\frac{T_2}{T_1}=1-\frac{290}{500}=0.42

Since efficiency is defined as;

η=workHeat\eta=\frac{work}{Heat}

0.42=W7000.42=\frac{W}{700}

W=294kJW=294kJ

Therefore it is impossible to have a work output greater than 294kJ and therefore the inventors claim is not reasonable.



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