To solve this problem, we need to calculate the efficiency of an ideal heat engine operating between the freezing and boiling points of water.$\\$The freezing point of water is $0^\circ$C, which is equivalent to $273$ K.$\\$The boiling point of water is $100^\circ$C, which is equivalent to $373$ K.$\\$The efficiency $\eta$ of an ideal (Carnot) heat engine is given by the formula:$\\ \eta = 1 - \frac{T_c}{T_h} \\$where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir.$\\$Substitute the known values:$\\ \eta = 1 - \frac{273}{373} \\$Calculate the fraction:$\\ \frac{273}{373} \approx 0.731 \\$Subtract from 1 to find the efficiency:$\\ \eta = 1 - 0.731 = 0.269 \\$Convert the efficiency to a percentage:$\\ \eta \times 100\% = 26.9\% \\$Therefore, the efficiency of the ideal heat engine is approximately $26.9\%$, which corresponds to Option 3.