Question

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

Answer 1

→COOLING EFFECT OF WATER
water can absorb large amount of heat to change its temp in very small amount. So it cools.
→COOLING EFFECT OF ICE=COOLING EFFECT OF WATER+
ice needs heat to melt
So ice absorbs more heat comparatively

Answer 2

"Ice at 273 Kelvin more effective in cooling than water at the same temperature.

  This is because, at 273 K or 0 degree Celsius temperature, the ice and water can interchange into each other.

  Hence, at 1 bar pressure, ice will melt to form a liquid phase which is water at 273K.

So, the "latent heat of fusion" for water at the temperature 0 degree Celsius, comes around 335 KJ/kg. Ice and water are the only two physical states of water.

  Here, ice is the "solid state of water" whereas water is the liquid state of it. The solid and liquid state can be converted into each other by changing the temperature. "