To determine the result of mixing 0.8 kg of ice at -10 °C with 0.8 kg of water at 80 °C, we need to consider the heat exchange that occurs during the process.
First, we need to calculate the amount of heat that needs to be transferred for the ice to reach its melting point (0 °C). We can use the specific heat capacity of ice, which is approximately 2.09 kJ/kg°C.
The heat transferred by the ice (Q_ice) can be calculated using the formula:
Q_ice = mass_ice * specific_heat_ice * temperature_change_ice
Where: mass_ice = 0.8 kg (mass of ice) specific_heat_ice = 2.09 kJ/kg°C (specific heat capacity of ice) temperature_change_ice = 0 °C - (-10 °C) = 10 °C (change in temperature from -10 °C to 0 °C)
Q_ice = 0.8 kg * 2.09 kJ/kg°C * 10 °C = 16.72 kJ
Next, we need to calculate the heat transferred by the water to reach the melting point (0 °C) and then heat it up to the final temperature.
The heat transferred by the water (Q_water) can be divided into two parts:
- Heat transferred to reach the melting point (0 °C): Q_water_melting = mass_water * specific_heat_water * temperature_change_water_melting
Where: mass_water = 0.8 kg (mass of water) specific_heat_water = 4.18 kJ/kg°C (specific heat capacity of water) temperature_change_water_melting = 0 °C - 80 °C = -80 °C (change in temperature from 80 °C to 0 °C)
Q_water_melting = 0.8 kg * 4.18 kJ/kg°C * -80 °C = -267.52 kJ
- Heat transferred to heat the water from 0 °C to the final temperature: Q_water_heating = mass_water * specific_heat_water * temperature_change_water_heating
Where: temperature_change_water_heating = final temperature - 0 °C = final temperature
Now, we can calculate the total heat transferred:
Total heat transferred = Q_ice + Q_water_melting + Q_water_heating
Since we don't have the final temperature specified in the question, we cannot calculate the exact result. However, we can determine the heat exchanged between the ice and water. The final temperature will be the point at which the heat exchanged by the ice and water balances out, resulting in thermal equilibrium.
The above calculations provide the necessary information to determine the total heat transferred during the process of mixing the ice and water. However, to find the final temperature and the state of the system after reaching equilibrium, we would need additional information or assumptions about the process, such as considering the system to be isolated or accounting for any heat loss to the surroundings.