Question

why is ice at 273k more effective in cooling the water at the same tempeature

Answer 1

this is because large amount of heat removed from ice than in case of water thus it cool more then water at 273 degree kelvin
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Answer 2

Ice at 273 K will absorb heat energy or latent heat from the medium to overcome the fusion to become water . So ice is more effective in cooling than water at the same temperature .