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 amount of ice melted, given that the ice cubes do not melt completely. 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 ⁻

Step-by-step solution

Since the ice cubes do not melt completely, the final temperature of the mixture is 0^ C . Mass of the drink is given by: m_d = V_d _d = 200 10⁻⁶ m ^3 1000 kg m ⁻³ = 0.2 kg Heat lost by the drink in cooling from 10^ C to 0^ C is: Q = m_d c_d T = 0.2 4200 (10 - 0) = 8400 J Let m be the mass of the ice melted. Assuming the initial temperature of the ice is 0^ C , the heat gained by the ice to melt is: Q = m L_f = m 3.4 10^5 J By the principle of calorimetry, heat lost by the drink equals heat gained by the ice: m 3.4