A cube of ice is taken from the freezer at -5.5 ∘C and placed in a 75-g aluminum calorimeter filled with 300 g of water at room temperature of 20.0 ∘C. The final situation is observed to be all water at 17.0 ∘C. The specific heat of ice is 2100 J/kg⋅C∘, the specific heat of aluminum is 900 J/kg⋅C∘, the specific heat of water is is 4186 J/kg⋅C∘, the heat of fusion of water is 333 kJ/Kg.
What was the mass of the ice cube?Express your answer to two significant figures and include the appropriate units.
Let mass of ice cube taken out be m kg .
ice will gain heat to raise its temperature from – 5.5° to 0° and then from 0° to 17° .
Total heat gained = m x 2.1 x 5.5 + m x 333 + m x 4.186 x 17
= (11.55 + 333 + 71.162 )m
= 415.712 m kJ
Heat lost by aluminium calorimeter
= .075 x .9 x 3
= .2025 kJ
Heat lost by water
= .3 x 4.186 x 3
Total heat lost
= 3.9699 kJ
Heat lost = heat gained
415.712 m = 3.9699
m = .0095 kg
9.5 gm .