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Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T_(1) and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T_(2). For what value of T the efficiencies of the two engines are equal.

Answer» <html><body><p>`(T_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) - T_(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))/(2)`<br/>`T_(1)T_(2)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(T_(1)T_(2))`<br/>`(T_(1) + T_(2))/(2)`</p>Solution :Efficiency of a carnot engine, `<a href="https://interviewquestions.tuteehub.com/tag/eta-446786" style="font-weight:bold;" target="_blank" title="Click to know more about ETA">ETA</a> = 1 - (T_(2))/(T_(1))` <br/> where `T_(1)` is the <a href="https://interviewquestions.tuteehub.com/tag/temperature-11887" style="font-weight:bold;" target="_blank" title="Click to know more about TEMPERATURE">TEMPERATURE</a> of source and `T_(2)` is the temperature of sink respectively. <br/> For engine A, `eta_(A) = 1 - (T)/(T_(1))` <br/> For engine B, `eta_(B) = 1 - (T_(2))/(T)` <br/> As per question, `eta_(A) = eta_(B)` <br/> As per question, `eta_(A) = eta_(B)` <br/> `:. 1 - (T)/(T_(1)) = 1 - (T_(2))/(T)` or `(T)/(T_(1)) = (T_(2))/(T)` <br/> or `T^(2) = T_(1)T_(2)` or `T = sqrt(T_(1)T_(2))`</body></html>


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