You’re right, ice has energy. If you consider a warm cup of water as a system and you add ice, the cup’s overall energy increases. The reaction that occurs when you add ice is called heat transfer. Since the water is warmer than the ice cubes, heat moves from the water to ice causing the molecules in the ice to vibrate faster and eventually changes it’s state to a liquid (solid molecules move slower than liquid molecules). I think this is the second law in thermodynamics.
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