An aluminium block of mass 840 g at a temperature of 200^ C is placed in a cavity within a large block of ice at 0^ C . The mass of ice that melts before the aluminium block cools down to 0^ C is x g . The value of x is ________. [Use: Specific heat capacity of aluminium = 900 J kg ⁻¹ K ⁻¹ , Latent heat of fusion of ice = 3.36 10^5 J kg ⁻¹ ]

Step-by-step solution

The final temperature of the aluminium block will be 0^ C since it is placed in a large block of ice. Heat lost by the aluminium block as it cools from 200^ C to 0^ C : Q = m_ Al s_ Al T Q = 0.84 900 200 Q = 151200 J This heat is entirely used to melt x g of ice at 0^ C . Heat gained by the ice: Q = m_ ice L 151200 = m_ ice 3.36 10^5 Solving for m_ ice : m_ ice = 151200 336000 = 0.45 kg Converting to grams: x = 0.45 1000 = 450 g Answer: 450