Question

why is ice at 273 more effective in cooling than water at the same temperature

Answer 1

Ice at 273 more effective in cooling than water at the same temperature as water contains the latent heat of fusion needed to overcome the interparticle forces of attraction whereas the ice doesn't contains any such heat and therefore when touched on any surface it soaks the heat of the surface to overcome the interparticle forces of attraction and also gain the latent heat of fusion.. .....
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Answer 2

Because at 0° C (273 K) particles of water have more energy comparing it to water at the same temperature.