To solve this problem, we need to use the formula for the efficiency of a Carnot engine.$\\$The efficiency $\eta$ of a Carnot engine is given by:$\\ \eta = 1 - \frac{T_{sink}}{T_{source}} \\$Given:$\\$• Efficiency $\eta = 50\% = 0.5 \\$• Source temperature $T_{source} = 327^\circ C \\$First, convert the source temperature to Kelvin:$\\ T_{source} = 327 + 273 = 600 \,$K$\\$Substitute the known values into the efficiency formula:$\\ 0.5 = 1 - \frac{T_{sink}}{600} \\$Rearrange to solve for $T_{sink}: \\ \frac{T_{sink}}{600} = 1 - 0.5 \\ \frac{T_{sink}}{600} = 0.5 \\ T_{sink} = 0.5 \times 600 \\ T_{sink} = 300 \,$K$\\$Convert the sink temperature back to Celsius:$\\ T_{sink} = 300 - 273 = 27^\circ C \\$Therefore, the temperature of the sink is $27^\circ C. \\$This corresponds to Option 1.