Question

A heat engine takes 100 J of heat from a hot reservoir and delivers 60 J of heat at a cold reservoir in one cycle. What would be the minimum temperature of the hot reservoir if the cold reservoir is at a temperature of 300 K ?

Answer 1

$$\begin{gathered} DearStudent, \\ TheefficiencyofCarnotengineintermsoftemperaturesofreservoirsisgivenby \\ \eta =\left(1-\frac{Q_{OUT}}{Q_{IN}}\right)\times 100\% \\ \eta =\left(1-\frac{60}{100}\right)\times 100\%=40\% \\ Also, \\ \eta =\left(1-\frac{T_L}{T_H}\right)\times 100\% \\ 40=\left(1-\frac{300}{T_H}\right)\times 100 \\ \frac{40}{100}=0.40=1-\frac{300}{T_H} \\ 0.40T_H=T_H-300 \\ {T}_H=500K \\ Henceminimumtemperatureofhotreserviourwillbe500K. \\ Regards \end{gathered}$$