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

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

• A. 35,490 kJ
• B. 21,775 kJ
• C. 53,107 kJ
• D. 189,756 kJ

Answer: (D)

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

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