Question

Why is water at 273K more effective in cooling than water at the same temperature?

Answer 1

There is something called Latent Heat. Latent Heat is required for phase transition from solid to liquid and from liquid to gas.Latent Heat of fusion is the energy required to change the phase from solid to liquid at melting point. Similarly Latent Heat of Vaporization is the energy required to change phase from liquid to gas at boiling point.
So, water at 273k has more energy as compared to ice at 273k ,since ice can easily absorb energy from surrounding in the from of latent heat to form water whereas water has no such privilege hence ice is more effective in cooling than water at same temperature.