To determine the result of mixing ice and water, we need to consider the energy exchange that occurs until thermal equilibrium is reached. We can assume that no heat is lost to the surroundings during the process. Here's a step-by-step approach to solving the problem:
Determine the heat gained or lost during the phase changes:
The ice at -10 °C needs to be heated to its melting point (0 °C). This requires energy given by: Q1 = (mass of ice) × (specific heat capacity of ice) × (change in temperature). Q1 = (0.8 kg) × (2,093 J/kg·°C) × (0 °C - (-10 °C)) Q1 = 16,744 J
The ice at 0 °C needs to melt into water at 0 °C. The energy required for this phase change is given by: Q2 = (mass of ice) × (latent heat of fusion of ice). Q2 = (0.8 kg) × (334,000 J/kg) Q2 = 267,200 J
The water at 0 °C needs to be heated to 80 °C. This requires energy given by: Q3 = (mass of water) × (specific heat capacity of water) × (change in temperature). Q3 = (0.8 kg) × (4,186 J/kg·°C) × (80 °C - 0 °C) Q3 = 26,688 J
Calculate the total energy exchanged: The total energy exchanged during the process is the sum of the three individual energy values: Total energy exchanged = Q1 + Q2 + Q3 Total energy exchanged = 16,744 J + 267,200 J + 26,688 J Total energy exchanged = 310,632 J
Determine the final temperature: The final temperature can be found by equating the energy gained by the ice to the energy lost by the water, assuming no energy loss to the surroundings: (mass of ice) × (specific heat capacity of ice) × (final temperature - 0 °C) = (mass of water) × (specific heat capacity of water) × (80 °C - final temperature) (0.8 kg) × (2,093 J/kg·°C) × (final temperature - 0 °C) = (0.8 kg) × (4,186 J/kg·°C) × (80 °C - final temperature) Solve this equation to find the final temperature.
By following these steps, you can determine the final temperature of the system after mixing the ice and water.