If a heater took 4 minutes to convert 500g of liquid water to 500g of water vapour how long would the same heater take to convert 500g of liquid aluminium to 500g of aluminium gas

It would take 8 mins

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