Question

If the initial temperature of the hot chocolate was is 180°F, what would the temperature of the drink be once the ice cubes had completely melted? Express your answer in "degrees Celsius" to one decimal place. Since the marshmallows were added after I served the drinks, they would have no impact on the temperature of the drink at the time I served it. Additional information is provided below.

From a purely personal perspective (i.e., in your own opinion), would you consider the chocolate milk still be too hot for you personally to drink or would it be a bit on the cool side? How can you support your answer?

Additional information:
Weight of ice cubes = 85 grams total weight
Initial temperature of ice cubes = - 22°C
Specific heat capacity of the hot chocolate = 3.751 kJ/kg C°

Hints: You can simplify things greatly if you draw a diagram to represent what is happening. Draw a vertical line to represent a "thermometer" and mark the important points on it (this diagram will also assist you in determining the temperature changes etc.). These points will include the starting temperatures of the chocolate milk and the ice as well as the freezing / melting point of the ice.

Let the final temperature of the thawed ice and milk be X (the chocolate milk and the melted ice will both have the same final temperature since they are mixed together in the same mug). X will be somewhere between the thawing / freezing point of the ice and the initial temperature of the milk - the trick is to find out what the temperature actually is. Remember that the heat lost by the milk will be equal to the heat gained by the ice, if we assume that no heat is lost to the surroundings (which we will do in this case).

If the initial temperature of the hot chocolate was is 180°F, what would the temperature of the drink be once the ice cubes had completely melted? Express your answer in "degrees Celsius" to one decimal place. Since the marshmallows were added after I served the drinks, they would have no impact on the temperature of the drink at the time I served it. Additional information is provided below.

From a purely personal perspective (i.e., in your own opinion), would you consider the chocolate milk still be too hot for you personally to drink or would it be a bit on the cool side? How can you support your answer?

Answer 1

Initial temperature of hot chocolate = 180° F

Let us convert it into °C

180°F = 82.2°C

Weight of ice cubes = 85 grams total weight
Initial temperature of ice cubes = - 22°C
Specific heat capacity of the hot chocolate = 3.751 kJ/kg C°

The heat absorbed by ice = Heat given by coffee

Let mass of coffee = 1000 grams (as it is not give, if it is known to you, you can replace the same in calcultion)

Heat absrobed by ice = Heat absorbed for going down temperaure of ice to 0C + heat of fusion + Heat of absorbed to raise the temperature of water from 0c to final temperature

Heat capacity of ice = 2.03 J / g C

Heat capacity of water 4.18 J / g C

Heat absrobed by ice = Mass of ice ( heat capacity of ice X change in temperature + Heat of fusion of ice + heat capacity of water X change in temperature) = Mass of coffee X specific heat of coffee X change in temperature

85 (2.03X (22) + 333.5 + 4.18 X (T2 - 0) ) = 1000 X (82.2 - T2) X 3.751

85(378.16 + 4.18 X T2) = 3751 (82.2 - T2)

378.16 + 4.18 T2 = 44.12 X 82.2 - 3751 T2

3755.18 T2 =3627.43

T2 = 0.96 C

This is can be considered for drinking puropose