Does the shape of a container affect the heat required to melt ice inside it?

[RingNebula57]

Hello everyone! I recently saw a problem about some ice in 2 containers. So:
We have 2 vertical cylindrical containers, which have perfect insulating walls, one with surface of the base S and the other one 2S , filled with the same mass of ice. The question is if there is any diffrence between the heat required to melt the ice in the 2 containers.
I would've probably said no , because Heat=(mass ice)*(latent heat of melting), and how the mass is the same then the heat does not differ. But the solution says that the heat required is diffrent , because if we melt all the ice , than it will turn completely into water , and because we have diffrent cross sections of the containters than the heat will differ. They arrived to that conclusion after saying that the diffrence in height between the initial center of mass and final center of mass for both systems differ.Then the diffrences of the potential energies is the 2 systems will differ also. And converting potential energy into heat we have diffrent heats.
And that seem alright too.
So why is my first guess incorrect?

Thank you!

 

[mfb]

Heat=(mass ice)*(latent heat of melting)

minus potential energy released in the process. Which is completely negligible for all practical purposes, but yes, it differs between the two containers. 10 centimeters (approximate difference if the ice is 1 or 2 meters high respectively) would give 1J/kg, compared to 330 kJ/kg the effect is 3 parts in a million.

 

[RingNebula57]

minus potential energy released in the process. Which is completely negligible for all practical purposes, but yes, it differs between the two containers. 10 centimeters (approximate difference if the ice is 1 or 2 meters high respectively) would give 1J/kg, compared to 330 kJ/kg the effect is 3 parts in a million.

Thank you!