To determine how much water will turn to ice, we need to calculate the amount of heat needed to freeze the water and compare it to the heat removed by the freezer motor.
The specific heat capacity of water is approximately 4.18 J/g°C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1°C.
The latent heat of fusion of water is approximately 334 J/g, which means it takes 334 Joules of energy to convert 1 gram of water at 0°C into 1 gram of ice at 0°C without changing its temperature.
Let's assume the freezer motor removes 500 J of heat from the water at 0°C.
First, we need to find out how much energy is required to freeze the water:
Energy required to freeze the water = mass of water × latent heat of fusion
Next, we'll find the mass of water:
Mass of water = Energy removed by the freezer motor ÷ specific heat capacity of water
Now, we can calculate the mass of water that will turn to ice:
Mass of water turned to ice = Energy required to freeze the water ÷ latent heat of fusion
Let's do the calculations:
Calculate the mass of water: Mass of water = 500 J ÷ 4.18 J/g°C ≈ 119.62 g
Calculate the energy required to freeze the water: Energy required to freeze the water = 119.62 g × 334 J/g ≈ 39,917.08 J
Calculate the mass of water that will turn to ice: Mass of water turned to ice = 39,917.08 J ÷ 334 J/g ≈ 119.62 g
So, approximately 119.62 grams of water will turn to ice after the freezer motor removes 500 J of heat from the water at 0°C.