How much heat is required to convert 3 kg of ice at -12°C to steam at 100°C?

To determine how much heat is required to convert 3 kg of ice at -12°C to steam at 100°C, we need to consider the various stages of the heating and phase change process that the ice undergoes. This involves several calculations based on specific heat capacities and latent heats of fusion and vaporization.

1. Heating the Ice from -12°C to 0°C:

The specific heat capacity of ice is approximately 2.09 kJ/kg·°C. To raise the temperature of 3 kg of ice from -12°C to 0°C, the calculation is:

[

Q_1 = m \cdot c_{\text{ice}} \cdot \Delta T = 3 , \text{kg} \times 2.09 , \text{kJ/kg°C} \times (0 - (-12)) , °C = 75.24 , \text{kJ}

]

2. Melting the Ice at 0°C:

The latent heat of fusion for ice is about 334 kJ/kg. To convert the 3 kg of ice at 0°C to water at 0°C, we use