Question

why is ice at 273K more effective in cooling than water at same temperatur

Answer 1

The ice has no latent ( hidden) heat of fusion I.e. the heat required to melt 1 kg of ice without increasing it's temp.
ice not having this energy has more potential to cool.
water at 0 temp. has latent heat of fusion thus it has some heat energy which ice doesn't have, thus ice is more effective in cooling than water at 0 ℃.

Answer 2

It is because ice has less kinetic energy than water. Therefore less energy will be used up which leads to cooling.

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