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In theory, the effectiveness of the cooling process depends on the ability/capacity of the cooling element (in this case, water and ice) to absorb energy from the system, until the system goes to equilibrium.

Ice is more effective than water in cooling liquids because ice needs additional energy to convert itself to water at 0ºC. Thus, it absorbs more heat from the liquid system it is in, making the liquid system cooler. In other words, ice at 0ºC is simply a "level" higher than water at 0ºC. The additional energy requirement is called "enthalpy of fusion.

Simple mathematical illustration:

X = Y + c

where:

X = energy that ice at 0ºC can absorb until equilibrium

Y = energy that water at 0ºC can absorb until equilibrium

c = constant (enthalpy of fusion)

Step by step mechanism is:

1. Ice at negative degrees Celsius absorbs energy to make the ice temperature 0ºC

2. Ice at 0ºC abosrbs energy to convert the ice to water (still at 0ºC)

3. Water at 0ºC absorbs energy until the system reaches equilibrium

Ice at 0ºC starts on step 2 while water at 0ºC starts on step 3.. Hope it can be of help..

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