At what speed should a piece of ice with a mass of 5 kg and an initial temperature of -100C

At what speed should a piece of ice with a mass of 5 kg and an initial temperature of -100C move to completely evaporate? It is known that 20% of the energy is spent on heating the environment.

Given: m = 5 kg; t0 = -100 ºС; η = 20% (0.2).

Constants: Сl = 2100 J / (kg * K); tmelt = 0 ºС; λ = 3.4 * 10 ^ 5 J / kg; Cw = 4200 J / (kg * K); tpap = 100 ºС; L = 2.3 * 10 ^ 6 J / kg.

Let us express the speed of movement of a piece of ice: η = m * (Сl * (tmelt – t0) + λ + Sv * (tpar – tm) + L) / (m * V ^ 2/2) = 2 * (Sl * (tm – t0) + λ + Sv * (tp – tm) + L) / V2; V = √ (2 * (Cl * (tm – t0) + λ + Sv * (tp – tm) + L) / η).

Calculation: V = √ (2 * (2100 * (0 – (-100)) + 3.4 * 10 ^ 5 + 4200 * (100 – 0) + 2.3 * 10 ^ 6) / 0.8) = 2859.2 m / s.