Specific heat question

Question

You order a 16 oz glass of tea (where the mass of Tea is 474 grams) from a local restaurant. The tea is freshly brewed and has an initial temperature of 28.16 °C. You add ice to cool it. If the heat of fusion of ice is 6.020 ^kJ/_mol and each ice cube contains exactly 1 mol of water (assume the ice does not add anymore volume), how many ice cubes are necessary to cool the tea to 4.90 °C? The specific heat of the "tea" is 4.184 ^J/_g°C. 

ice cubes (partial cubes allowed) and ignore the heat required to raise the temperature of the melted ice cubes

Answer 1

To find the amount of ice cubes needed to change the temperature of the tea to 4.90 C you would have to find the heat energy that is transferred from the tea when the ice cubes are added (Q). You would then divide your heat energy value that you found by the specific heat of ice to determine how many ice cubes you need. The specific heat refers to the amount of heat needed to raise one unit mass of a substance by one degree. The specific heat of ice tells you how much heat energy is absorbed by one ice cube.

Q = 

Q= heat energy released from the tea when it is cooled to the desired temperature.

C=specific heat of your tea. We can use the specific heat of water because the tea is mostly water.

delta T= temperature change of your tea

m=mass of your tea

Q=(474g)*(4.184 J/g*C)*(28.16C-4.90C)=46129.6 J

46129.6 J of heat energy is lost from the tea.

Convert specific heat of ice to joules from kilojoules: (6.020 kj/mol)*(1000 J/1 Kj)=6020 J

(46129.6 J)/(6020 J)= 7.66

7.66 ice cubes are needed.