The change in entropy ($\Delta S$) during a phase transition at a constant temperature is given by the formula: $\Delta S = \frac{q_{rev}}{T}$ where $q_{rev}$ is the heat absorbed reversibly and $T$ is the absolute temperature .

1. Calculate Heat Absorbed ($q$): The heat required to melt mass $m$ is given by $q = m \times L_f$, where $L_f$ is the latent heat of fusion. Given: $m = 1 \text{ kg} = 1000 \text{ g}$ and $L_f = 80 \text{ cal/g}$. $q = 1000 \text{ g} \times 80 \text{ cal/g} = 80,000 \text{ cal}$

2. Convert Temperature to Kelvin: $T = 0^{\circ}\text{C} = 273 \text{ K}$

3. Calculate Entropy Change ($\Delta S$): $\Delta S = \frac{80,000 \text{ cal}}{273 \text{ K}} \approx 293 \text{ cal/K}$