Calculating the heat required to convert 3 kg of ice at -12 degrees Celsius to steam at 100 degrees Celsius involves several steps. We will calculate the heat required to raise the temperature of the ice to 0 degrees Celsius, then the heat required to melt the ice into water, then the heat required to raise the temperature of the water to 100 degrees Celsius, and finally the heat required to convert the water into steam.

Step 1: Heating the ice to 0 degrees Celsius:
The specific heat capacity of ice is given as 2100 J/kg/K. As the ice is at -12 degrees Celsius, we need to raise its temperature to 0 degrees Celsius. The formula to calculate the heat required is:

Heat = mass * specific heat capacity * temperature change
Heat = 3 kg * 2100 J/kg/K * (0 - (-12) K)
Heat = 3 kg * 2100 J/kg/K * 12 K
Heat = 75,600 J

So, the heat required to raise the temperature of the ice to 0 degrees Celsius is 75,600 J.

Step 2: Melting the ice into water:
The latent heat of fusion of ice is given as 3.35 J/kg. This represents the heat required to convert 1 kg of ice at 0 degrees Celsius into water at 0 degrees Celsius. Since we have 3 kg of ice, the total heat required to melt the ice is:

Heat = mass * latent heat of fusion
Heat = 3 kg * 3.35 J/kg
Heat = 10.05 J

So, the heat required to melt the ice into water is 10.05 J.

Step 3: Heating the water to 100 degrees Celsius:
The specific heat capacity of water is given as 4186 J/kg/K. We need to raise the temperature of the water from 0 degrees Celsius to 100 degrees Celsius. The formula to calculate the heat required is:

Heat = mass * specific heat capacity * temperature change
Heat = 3 kg * 4186 J/kg/K * (100 - 0) K
Heat = 1,255,800 J

So, the heat required to raise the temperature of the water to 100 degrees Celsius is 1,255,800 J.

Step 4: Converting the water into steam:
The latent heat of steam is given as 2.256 J/kg. This represents the heat required to convert 1 kg of water at 100 degrees Celsius into steam at 100 degrees Celsius. Since we have 3 kg of water, the total heat required to convert the water into steam is:

Heat = mass * latent heat of steam
Heat = 3 kg * 2.256 J/kg
Heat = 6.768 J

So, the heat required to convert the water into steam is 6.768 J.

Total heat required:
To find the total heat required, we add up the heats calculated in each step:

Total heat required = Heat step 1 + Heat step 2 + Heat step 3 + Heat step 4
Total heat required = 75,600 J + 10.05 J + 1,255,800 J + 6.768 J
Total heat required = 1,338,218.818

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