Final answer:
To determine the time it will take for the ball of ice to completely melt, we need to consider the heat transfer between the ice and the water. First, calculate the amount of heat required to raise the temperature of the ice from 0°C to its melting point. Next, calculate the amount of heat required to melt the ice completely. Finally, determine the total time it will take for the ice to completely melt by dividing the total heat required by the rate at which heat is transferred.
Step-by-step explanation:
To determine the time it will take for the ball of ice to completely melt, we need to consider the heat transfer between the ice and the water.
First, we can calculate the amount of heat required to raise the temperature of the ice from 0°C to its melting point, which is also 0°C. We can use the formula:
Q = mcΔT
where Q is the heat transferred, m is the mass of the ice, c is the specific heat capacity of ice, and ΔT is the change in temperature.
Next, we can calculate the amount of heat required to melt the ice completely. We can use the formula:
Q = mL
where Q is the heat transferred, m is the mass of the ice, and L is the latent heat of fusion for ice.
Finally, we can determine the total time it will take for the ice to completely melt by dividing the total heat required by the rate at which heat is transferred. The rate of heat transfer can be calculated using the formula:
Q = kAΔT/t
where Q is the heat transferred, k is the thermal conductivity of water, A is the surface area of the ice, ΔT is the temperature difference between the ice and the water, and t is the time taken.