Final answer:
The temperature of water as it freezes and the temperature of ice as it melts are the same — 0°C under standard pressure. This is the point of thermal equilibrium where both phases can coexist. With no external temperature change, ice in 0°C water in an insulated container will not melt or freeze further.
Step-by-step explanation:
The temperature of water as ice begins to form and the temperature of ice as it begins to melt is essentially the same, this is known as the freezing point or melting point of water.
When water transitions from a liquid to a solid (freezing), the temperature can slightly increase due to the heat released during the freezing process, and then holds constant at the freezing point. Conversely, when ice begins to melt, it must absorb a significant amount of heat without a change in temperature (latent heat of fusion) until all the ice has converted into liquid water.
In a typical scenario at standard atmospheric pressure, this temperature is 0°C. Both processes - the formation of ice and the melting of ice - occur at this temperature in what is known as thermal equilibrium, as long as there is ice in contact with water in the system. Once all of the ice melts, the temperature of the liquid water will start to rise if the heat continues to be supplied. Similarly, once all the water has frozen, the temperature of the ice will begin to drop if the environment continues to remove heat from the system.
Thus, with 0°C ice placed in 0°C water in an insulated container, the system remains in equilibrium, and neither additional ice melting nor water freezing will take place unless the external conditions change.