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Answer #1:
125 grams of water (which is also 125 milliliters, or 125 cubic centimeters) requires 125 calories of heat to raise the temperature 1 degree Celsius. Note that calories are an energy source, and heat is a form of energy. If the ice is 1 degree from the melting point, it would take approximately 125 calories to bring the entire mass to the melting point to melt the ice. Granted, that is if the ice is in a completely closed system. Normally, air flow near the region will cause heat to disperse, carrying away the warmest regions of heat...requiring more heat (calories).
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Answer #2:
The first answer completely misses one of the most important and unique properties of water.
If you have 1 cubic centimeter of ice at 0°C, it takes about 80 calories of heat
just to melt it into water with no change in temperature.
To melt 125 g of ice, you need 9,972 calories of heat energy. And then, the
temperature of the 125 g of water that you have is still 0°C, but now it's water.
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