Excess ice at 0°C is placed in an insulated cup containing 361 g of soft drink at 23°C. The specific heat of the drink is the same as that of water (4.184 J/g°C).

Question

Excess ice at 0°C is placed in an insulated cup containing 361 g of soft drink at 23°C. The specific heat of the drink is the same as that of water (4.184 J/g°C). Some ice remains after the drink cools to 0°C. Determine the mass of ice that has melted. Assume that the heat capacity of the cup can be ignored. It takes 334 J to melt 1.00 g of ice at 0°C.

Consider the ice as the system and the water as the surroundings or vice versa. Either way, realize that the heat is being transferred from the soft drink (source of thermal energy) to the ice (the sink of thermal energy).

Please show steps.

Answer 1

In order to cool 361g of the drink from 23˚ to 0˚, it needs to lose a certain amount of heat energy to the ice, calculated as follows (notice how the units cancel to leave the result in joules):

Q=mcΔT = (361g)(4.184 J/g˚C)(23˚C - 0˚C) = 34,739.75 J

Next, if we know how much energy is required to melt 1g of ice (334 J), we can figure out how many grams will melt:

34,739.75 J × (1.00g / 334 J) = 104.01 g