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Consider a drink with ice in it. Room temperature is warmer than the drink, so just by being in the room (or even worse, in your warm hand) the drink is going to absorb a certain amount of heat energy which tends to increase its temperature. However, any temperature higher than the melting point of water (0o Celsius) is going to melt the ice. And since it takes energy to melt ice, that energy cannot raise the temperature until the ice is all melted.

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