Question

A cube of ice is taken from the freezer at -8.5 ∘C and placed in a 95-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?

Answer 1

To find the mass of the ice cube, you need to calculate the heat transfer between the ice cube and the water, the heat transfer from the water to the aluminum calorimeter, and then use the equation Q₁ + Q₂ = 0 to find the mass of the ice cube.

Step-by-step explanation:

To find the mass of the ice cube, we need to use the principle of conservation of energy.

First, we need to calculate the heat transfer between the ice cube and the water, using the equation Q = mcΔT, where Q is the heat transfer, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Since the final situation is observed to be all water at 17.0°C, we can calculate the heat transfer from the ice cube to the water using:

Q₁ = mcΔT = (mass of ice)(specific heat of ice)(change in temperature of ice)

Next, we need to calculate the heat transfer from the water to the aluminum calorimeter using:

Q₂ = mcΔT = (mass of water)(specific heat of water)(change in temperature of water)

Finally, we need to use the equation Q₁ + Q₂ = 0 to find the mass of the ice cube.

Answer 2

The mass of the ice cube is 13.33 g.

Step-by-step explanation:

To determine the mass of the ice cube, we need to calculate the heat transferred from the ice to the water and the calorimeter. First, we calculate the heat transferred from the ice using the formula: ΔQ = m * L_f, where m is the mass of the ice and L_f is the heat of fusion of water. The heat transferred from the water and the calorimeter can be calculated using the formula: Q = m * c * ΔT, where m is the mass of the water and c is the specific heat capacity of water. By equating the heat transferred from the ice to the heat transferred from the water and the calorimeter, we can solve for the mass of the ice cube.

Using the given values:

• Specific heat capacity of ice, c_ice = 2100 J/kg*C
• Specific heat capacity of aluminum, c_aluminum = 900 J/kg*C
• Specific heat capacity of water, c_water = 4186 J/kg*C
• Heat of fusion of water, L_f = 333,000 J/kg
• Mass of aluminum calorimeter, m_aluminum = 95 g
• Mass of water, m_water = 300 g
• Initial temperature of water, T_water_initial = 20*C
• Final temperature of water, T_water_final = 17*C
• Final temperature of the system, T_final = 17*C

We can use the formula Q = m * c * ΔT to calculate the heat lost by the water and the calorimeter:

Q_water_calorimeter = (m_water + m_aluminum) * c_water * (T_water_initial - T_final)

We can use the formula Q = m * c * ΔT to calculate the heat gained by the ice:

Q_ice = m_ice * c_ice * (T_final - 0*C)

We can use the formula Q = m * L_f to calculate the heat absorbed during the ice melting:

Q_melting = m_ice * L_f

By equating these three equations, we can solve for the mass of the ice cube:

Q_ice + Q_melting = Q_water_calorimeter

m_ice * c_ice * (T_final - 0*C) + m_ice * L_f = (m_water + m_aluminum) * c_water * (T_water_initial - T_final)

After solving this equation, we find that the mass of the ice cube is 13.33 g.