A $0.360 \mathrm{kg}$ piece of solid lead at $20^{\circ} \mathrm{C}$ is placed into an insulated container holding $0.980 \mathrm{kg}$ of liquid lead at $420^{\circ} \mathrm{C} .$ The system comes to an equilibrium temperature with no loss of heat to the environment. Ignore the heat capacity of the container. (a) Is there any solid lead remaining in the system? (b) What is the final temperature of the system?