The entropy of mixing hot and cold water

$0.80\ \text{kg}$ of water at $85\ ^\circ\text{C}$ is mixed with different amounts of water at $12\ ^\circ\text{C}$, from $0.2\ \text{kg}$ to $3.0\ \text{kg}$. You will make the program find the final temperature and the total change of entropy for each amount, and how much cold water brings the mix to $40\ ^\circ\text{C}$.

The idea. The final temperature is the mass-weighted average. Each part changes its entropy by $mc\ln\dfrac{T_f}{T}$, with temperatures in kelvin. The second law says the total must rise.

Your tasks.

1. Work out Tf, the final temperature in kelvin for every cold mass in m.
2. Work out dS, the total change of entropy for every cold mass.
3. Work out m40, the cold mass that makes the final temperature $40\ ^\circ\text{C}$.