When ice melts then change in internal energy

When ice melts then change in internal energy is greater than the heat supplied, why?

When ice melts, volume of water formed is less than that of ice. So, surroundings (environment) does work on the system (ice). And by first law, ∆Q = ∆ W + ∆U
∆U = ∆Q - ∆ W
(∆ W= negative as work is done on the system)
∆U > ∆Q