Mixing hot and cold water

Hot water at $80\ ^\circ\text{C}$ is poured into $0.60\ \text{kg}$ of water at $15\ ^\circ\text{C}$ in an aluminium calorimeter of mass $0.20\ \text{kg}$. You will make the program find the final temperature for different amounts of hot water, with and without the calorimeter, and the amount that gives $40\ ^\circ\text{C}$.

The idea. Heat lost $=$ heat gained. The calorimeter adds its water equivalent, $\dfrac{m_cc_c}{c_w}$, to the cold water.

Your tasks.

1. Work out T_plain, the final temperature for each mass of hot water, ignoring the calorimeter.
2. Work out the calorimeter's water equivalent w, and T_real, the final temperature allowing for it.
3. Find the mass of hot water that brings the real mixture to $40\ ^\circ\text{C}$.