Why does hot water clean dishes better than cold?

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ill take a stab:
The kinetic energy of all those hot water molecules is going to dislodge many more dirt particles off of the surface of dishes, when compared with the effect of cold water molecules.
Come to think of it, isn't temperature a measure of the root mean square momentum of the particles?

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well, all those fats were probably hot at one point and liquid/gelatinous. if you reheat them they will probably go from the solid state to a more gelatinous one and be easier to get rid of