How much energy is required to raise 63 kg of ice at 0 degrees C to saturated steam at 100 degrees C?

To determine the total energy needed to convert 63 kg of ice at 0 degrees Celsius to saturated steam at 100 degrees Celsius, we must consider several stages of the phase change and heating process.

Firstly, ice at 0 degrees Celsius must be melted into water at 0 degrees Celsius. The latent heat of fusion for ice is approximately 334 kJ/kg. So, the energy required to melt 63 kg of ice is:

( Q_{melting} = mass \times L_f )

( Q_{melting} = 63 kg \times 334 kJ/kg = 21,042 kJ )

Next, the water must be heated from 0 degrees Celsius to 100 degrees Celsius. The specific heat capacity of water is about 4.18 kJ/kg°C. Thus, the energy required to heat the water is:

( Q_{heating} = mass \times c \times \Delta T )

( Q_{heating} = 63 kg \times 4.18 kJ/kg°C \times (100°C - 0°C) = 26,314 kJ )

Then, we need to vaporize the water at 100 degrees Celsius into steam. The latent