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The way to make an ice cube is to fill a container with water at room temperature (20 degree Centigrade, say) and then put the container in a freezer, which removes heat from the container/water until the water temperature is below the freezing point (0 degree C, approximately, depending on the atmospheric pressure and water purity). So, the temperature of an ice cube is at or below zero degree C -- something that cannot be achieved outside the freezer.

Now take the ice cube out of container and place it on table top. The air and the table surface that the ice cube is in contact are pretty much at 20 degree C temperature. The ice cube starts absorbing the heat from its surrounding. The outer skin will melt first, because its temperature is now above zero degree C, until the whole ice cube becomes a puddle of water. If you touch the puddle just after the ice disappears, you can feel that the water is cooler than the air, because the heat absorption is incomplete. Wait an hour or so, and the water will be at the same temperature as the room air.

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Q: Why does an ice cube melt at rom temp?
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