Heat is a form of energy (or a result/expression of energy, if you like). The liquid drink has some energy (heat) in it, and the ice cubes have less energy (heat) in them. When you put the ice cubes in the drink, the energy wants to equalize, so energy (heat) moves from the higher-energy material (the drink) into the lower-energy material (the ice) until they’re roughly equal, which melts the ice.
I think you are misunderstanding energy as a workforce.
Energy itself doesn’t do “work”.
Difference of the energy does.
If the surrounding air is 500 degree, shoving coals that burn at 500 degree won’t do any work.
What happens with dropping ice cube in the cup is like digging a deep hole in a sand dune. It takes energy from surrounding and equalize, which is kinda work.
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