Ice at 273 K (0°C) is more effective in cooling than water at the same temperature because it requires more energy to melt ice into water than to simply raise the temperature of water.
When ice is placed in contact with a warmer object, such as a warm beverage, the ice absorbs heat from the beverage in order to melt into water. This heat absorbed by the ice is called the heat of fusion. This process requires a significant amount of energy, as the heat of fusion of water is approximately 334 joules per gram.
In contrast, when water at 273 K is placed in contact with a warm object, it can only absorb heat by its temperature rising. The specific heat capacity of water is approximately 4.18 joules per gram per degree Celsius, which is much lower than the heat of fusion of ice.
Therefore, ice at 273 K is more effective in cooling than water at the same temperature because it can absorb a greater amount of heat energy from a warm object due to the heat of fusion required to melt the ice.