Final answer:
The problem is about finding the final temperature of a mixture of ice and water, taking into account the heat transfer between them. The essential concepts include conservation of energy, specific heats, and the enthalpy of fusion for ice.
Step-by-step explanation:
The question involves the transfer of heat between ice and water until they reach a final temperature at equilibrium. To solve for the final temperature, we can use the concept of conservation of energy. The heat lost by the water as it cools will be equal to the heat gained by the ice as it warms up and possibly melts. The specific heat of ice is 2.062 J/(g°C), and the specific heat of liquid water is 4.184 J/(g°C). The enthalpy of fusion of ice is 6.01 kJ/mol, which is also the energy required to melt ice at 0°C into water at 0°C. To find the final temperature, we calculate the amount of energy required to melt the ice and then see if the water has sufficient heat to fully melt the ice and still change the temperature of the mixture. If it does, we proceed to calculate the new equilibrium temperature after melting.