t₁ = time to convert liquid water to water vapor = 4 min = 4 x 60 = 240 sec
t₂ = time to convert liquid aluminium to aluminium gas = 4 min = ?
m₁ = mass of water = 500 g = 0.5 kg
L₁ = latent of vaporization = 2260000 J/kg
m₂ = mass of aluminium = 500 g = 0.5 kg
L₂ = latent of vaporization of aluminium = 10530000 J/kg
using conservation of heat
m₁ L₁ /t₁ = m₂ L₂ /t₂
(0.5) (2260000)/240 = (0.5) (10530000)/t₂
t₂ = 1118.23 sec
t₂ = 18.6 min
