A Carnot engine has an efficiency of 50%50\%50% when its source is at a temperature 327∘C327^\circ\text{C}327∘C. The temperature of the sink is
27∘C27^\circ\text{C}27∘C
15∘C15^\circ\text{C}15∘C
100∘C100^\circ\text{C}100∘C
200∘C200^\circ\text{C}200∘C
Efficiency η=1−T2T1\eta = 1 - \frac{T_2}{T_1}η=1−T1T2. Given η=0.5\eta = 0.5η=0.5 and T1=327+273=600KT_1 = 327 + 273 = 600 \text{K}T1=327+273=600K. So, 0.5=1−T2600 ⟹ T2600=0.5 ⟹ T2=300K0.5 = 1 - \frac{T_2}{600} \implies \frac{T_2}{600} = 0.5 \implies T_2 = 300 \text{K}0.5=1−600T2⟹600T2=0.5⟹T2=300K. Converting to Celsius, T2=300−273=27∘CT_2 = 300 - 273 = 27^\circ\text{C}T2=300−273=27∘C.
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