Heating ice to steam

A $1.2\ \text{kW}$ heater warms $0.50\ \text{kg}$ of ice from $-20\ ^\circ\text{C}$ until it is all steam at $100\ ^\circ\text{C}$. You will make the program find the heat and the time for each stage, and which stage takes longest.

The idea. Warming: $mc\,\Delta T$ (ice $2100\ \text{J kg}^{-1}\text{K}^{-1}$, water $4186\ \text{J kg}^{-1}\text{K}^{-1}$). Changes of state: $mL$ ($L_f = 3.34 \times 10^{5}\ \text{J/kg}$, $L_v = 2.26 \times 10^{6}\ \text{J/kg}$). Time $= \dfrac{\text{heat}}{P}$.

Your tasks.

1. Work out Q, the heat for each of the four stages, in the order of names.
2. Work out t, the time for each stage.
3. Find the total time, and the name of the longest stage.