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There is nothing special about alcohol -- anything that is in contact with ice that is warmer than 0 °C will melt ice cubes (as long as the mass of warm object is comparable to the mass of the ice -- obviously a cup of warm water won't melt the ice on an entire lake for instance).

When two objects of different temperatures are put in contact (as when you put ice cubes in a drink), the warmer one will always transfer heat to the cooler one. If the warmer one transfers enough heat to melt the ice cubes, then they melt! If not, they might just partially melt.

It's actually possible to add ice cubes to alcohol and not have them melt at all! The freezing point of alcohol is well below 0 °C, and so you can have liquid alcohol be much colder than frozen ice cubes. If you add an ice cube to alcohol that is colder than the ice cube, the ice cube will be cooled by the alcohol!

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Q: What causes alcohol to melt ice cubes?
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