Calculation of the amount of water needed to melt the ice

To calculate the amount of water needed to melt the ice, we need to consider the heat transfer that occurs during the process. The heat transfer equation can be expressed as:

Q = m * L

Where:
Q is the amount of heat transferred
m is the mass of the substance
L is the latent heat of fusion

In this case, we have 2.2 kg of ice that needs to be melted. The latent heat of fusion for ice is approximately 334 kJ/kg.

Step 1: Calculate the heat transfer required to melt the ice

Q = m * L
Q = 2.2 kg * 334 kJ/kg
Q = 734.8 kJ

Therefore, 734.8 kJ of heat transfer is required to melt the 2.2 kg of ice.

Step 2: Calculate the amount of water needed

Since we want to determine the amount of water at 50 degrees Celsius needed to melt the ice, we need to consider the heat transfer between the water and the ice. The heat transfer equation can be expressed as:

Q = m * c * ΔT

Where:
Q is the amount of heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature

Step 3: Determine the specific heat capacity of water

The specific heat capacity of water is approximately 4.18 kJ/kg °C.

Step 4: Calculate the temperature change of the water

The water needs to cool down from 50 degrees Celsius to 0 degrees Celsius, resulting in a temperature change of 50 degrees.

Step 5: Calculate the mass of water needed

Q = m * c * ΔT
734.8 kJ = m * 4.18 kJ/kg °C * 50 °C

Simplifying the equation:
734.8 kJ = m * 209 kJ/kg
m = 3.51 kg

Therefore, approximately 3.51 kg of water at 50 degrees Celsius is needed to just melt the 2.2 kg of ice at 0 degrees Celsius.