Final answer:
Heat flow will cease when thermal equilibrium is attained between the ice and its surroundings. This occurs when the ice completes melting and the meltwater reaches the temperature of the environment. The change in heat, dictated by the enthalpy of fusion, is balanced to keep the entropy of the universe constant.
Step-by-step explanation:
The heat flow will stop when the temperature of the ice reaches equilibrium with the surroundings, which is when the ice finishes melting and the meltwater warms up to the temperature of its environment. According to the second law of thermodynamics, heat flow cannot spontaneously transfer energy from a cooler object to a hotter one; it only flows until thermal equilibrium is reached.
In the example of ice melting at 0°C on high thermal conductivity carbon foam, heat flow occurs until the absorbed heat raises the temperature of the meltwater to match the carbon foam's temperature. The enthalpy of fusion dictates the amount of heat required for the ice to melt. The entropy of the universe remains unchanged in this reversible process, as the gain of heat by the ice matches the loss of heat from the surroundings.
Various examples show the practical application of these principles, such as determining how much ice melts in a foam icebox kept at a higher temperature, or calculating the change in temperature when an ice cube is added to a drink. These examples use the general formula relating heat gained and heat lost, incorporating the specific heat and the enthalpy of fusion when necessary.