To determine the final temperature of the water after the ice has melted, we need to consider the heat transfer that occurs during the process.
First, let's calculate the heat absorbed by the ice to melt it:
Heat absorbed by the ice = mass of ice × latent heat of fusion = 1 kg × 336,000 J/kg = 336,000 J
Next, let's calculate the heat lost by the water to cool down:
Heat lost by the water = mass of water × specific heat capacity of water × change in temperature = 9 kg × 4,186 J/kg·°C × (50°C - final temperature)
Since the ice melts and the final temperature of the water is the same, the heat absorbed by the ice is equal to the heat lost by the water:
336,000 J = 9 kg × 4,186 J/kg·°C × (50°C - final temperature)
Now we can solve for the final temperature:
336,000 J = 37,674 J/°C × (50°C - final temperature)
Dividing both sides by 37,674 J/°C:
336,000 J / 37,674 J/°C = 50°C - final temperature
8.93°C = 50°C - final temperature
Rearranging the equation to solve for the final temperature:
final temperature = 50°C - 8.93°C = 41.07°C
Therefore, the final temperature of the water after the ice has melted will be approximately 41.07°C.