3. A calorimeter has a mass of 100g and a specific heat of 0.900 cal/g˚C and contains 400g of water at 40˚C. When 91g of ice at 0.0˚C is added and completely melted, the temperature of the water is 18.2˚C. Calculate the heat fusion of the ice
To calculate the heat fusion of the ice, you need to determine the amount of heat transferred during the process of melting the ice. This can be done by considering the change in temperature of the water in the calorimeter.
First, calculate the initial heat absorbed by the water in the calorimeter before the ice is added:
Q1 = mass_water * specific_heat_water * (final_temperature_water - initial_temperature_water)
mass_water = 400g
specific_heat_water = 1 cal/g˚C (specific heat of water)
final_temperature_water = 18.2˚C
initial_temperature_water = 40˚C
Q1 = 400g * 1 cal/g˚C * (18.2˚C - 40˚C)
Next, calculate the heat absorbed by the calorimeter:
Q2 = mass_calorimeter * specific_heat_calorimeter * (final_temperature_water - initial_temperature_water)
mass_calorimeter = 100g
specific_heat_calorimeter = 0.900 cal/g˚C (specific heat of the calorimeter)
final_temperature_water = 18.2˚C
initial_temperature_water = 40˚C
Q2 = 100g * 0.900 cal/g˚C * (18.2˚C - 40˚C)
Since Q1 and Q2 represent the total heat absorbed during the process, the heat transferred during the melting of the ice is equal to their sum:
Q_fusion = Q1 + Q2
Calculate Q_fusion to get the value for the heat fusion of the ice.