Final answer:
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.