Four 2 cm 2 cm 2 cm cubes of ice are removed from a refrigerator and placed in 200 ml of a drink at 10^ C . Determine the temperature of the drink once thermal equilibrium is reached. Assume that the container has negligible heat capacity and no heat is lost to the surroundings of the drink. Density of ice = 900 kg m ⁻³ , density of the drink = 1000 kg m ⁻³ , specific heat capacity of the drink = 4200 J kg ⁻¹ K ⁻¹ ,

Step-by-step solution

Volume of the four ice cubes is V_ ice = 4 (2 2 2) = 32 cm ^3 = 32 10⁻⁶ m ^3 . Mass of the ice is m_ ice = V_ ice _ ice = 32 10⁻⁶ 900 = 0.0288 kg . Mass of the drink is m_ drink = V_ drink _ drink = 200 10⁻⁶ 1000 = 0.2 kg . Assuming the initial temperature of the ice is 0^ C , the heat required to melt all the ice is Q_ req = m_ ice L = 0.0288 3.4 10^5 = 9792 J . The maximum heat that can be released by the drink in cooling from 10^ C to 0^ C is Q_ rel = m_ drink c_ drink T = 0.2 4200 10 = 8400 J . Since Q_ rel The