Final answer:
Hot coffee is cooled by an ice cube through conduction and phase change, as heat is transferred from the coffee to the ice, causing it to melt and the coffee to cool until thermal equilibrium is reached.
Step-by-step explanation:
An ice cube cools hot coffee through the process of heat transfer, specifically through conduction and phase change. When an ice cube is introduced to hot coffee, energy in the form of heat is transferred from the warmer coffee to the colder ice cube. This heat causes the ice to undergo a phase transformation from solid (ice) to liquid (water) as expressed by the thermochemical equation: heat + H₂O(s) → H₂O(l).
During this process, the heat (Qice) transferred to the ice not only is used for the phase change, represented by Qice = mice Lf (melting of the ice), but also raises the temperature of the melted water up to the equilibrium temperature (T'). The coffee, in turn, loses an equal amount of heat (Qcoffee), which results in the coffee cooling down. The process continues until thermal equilibrium is reached between the coffee and the melted ice, which means both substances reach the same temperature.