Final answer:
A cup of water with an ice cube at 0°C maintains its temperature due to thermal equilibrium and the enthalpy of fusion during the phase change of ice to water, which absorbs heat without raising the water's temperature.
Step-by-step explanation:
When a cup of water contains an ice cube at 0°C, the system is said to be in thermal equilibrium. As a result, the temperature remains constant at the freezing point, which is 0°C. This is because as long as there is ice in the water, the heat that enters the water from the surrounding environment is used to melt the ice, rather than to increase the water's temperature.
The process of ice melting is an example of a phase change, where ice (solid water) turns into liquid water. This phase change absorbs heat without raising the temperature, a concept known as the enthalpy of fusion. Thus, on a hot summer day, a cup of water or soda with ice cubes stays at 0°C because the heat from the hot environment continues to melt the ice, rather than increase the temperature of the water.
Once all the ice has fully melted, there is no more phase change to absorb the heat, and the water's temperature will begin to rise if more heat is added to the system.