system
Given the following post, respond as if you're commenting on Reddit:
human
Does the amount of time it takes an ice cube to melt directly proportional to it's temperature?

Would an ice cube that had been stored at 0 degrees F melt more slowly than one that had been stored at 10 F?  If so, what's the mathematical nature of this relationship?
Edit: Apologize for the grammar in my title.
gpt
It's not directly proportional.

There are two things that need to happen for ice to melt:

1. The ice needs to be heated to the melting point of 0C
2. The ice then needs to gain energy to overcome the enthalpy of fusion, in a similar way that boiling water needs extra energy to go from a liquid at 100C to a gas (steam) at 100C.

The specific heat capacity of ice is ~2.1 J g^-1 K^-1. In other words, to raise 1g of ice by 1C (or 1K) you'd need 2.1 joules to do it.

To turn 1g of ice at 0C into 1g of water at 0C you'd need to add 334.774 J. This is approximately 160x the amount of energy needed to heat it up by 1C. So unless the temperature difference is very high, the difference in the time to melt will be fairly insignificant.

You've also got to consider other factors, like the fact that heat exchange will depend on the surface area, as well as the temperature difference (a larger difference will generally mean more rapid heat transfer).