on a hot summer's day after sitting on a table in the sun for several hours, a jug of juice has reached a temperature of 33C. 0.48 kg of the drink is poured into an insulated travel mug, and two ice cubes at a temperature of 0C and with a mass of 0.050 kg each are added. Assume that no heat is exchanged between the contents of the travel mug and the surroundings and that the thermal properties of the juice are the same as those of water. Specific heat for water is 4.18 kJ/(kg K) and latent heat is L = 333.5 kJ/kg (a) Derive an expression for the heat lost by the juice in terms of its final temperature. (b) Derive an expression for the heat gained by the ice cubes and resulting water. (c) Calculate the final temperature of the juice. (d) What would the final temperature of the juice be if 12 ice cubes had been added instead of 2? (e) Comment on your answer to part (d) and explain what the result means in terms of the final temperature. (f) How much ice is needed to cool the juice to 0C? What does that tell us about adding more ice cubes?