To determine the mass of steam required to heat 1 kg of ice until it boils, we need to consider the energy required for each phase change.
- Heating the ice from its initial temperature to its melting point: The specific heat capacity of ice is approximately 2.09 kJ/kg°C. The initial temperature is 0°C, and the melting point of ice is 0°C. Therefore, the energy required to heat 1 kg of ice from 0°C to 0°C (melting point) is:
Q1 = mass × specific heat capacity × temperature difference Q1 = 1 kg × 2.09 kJ/kg°C × (0°C - 0°C) Q1 = 0 kJ
No energy is required for this phase change, as the ice is already at its melting point.
- Melting the ice into water: The latent heat of fusion for ice is approximately 334 kJ/kg. This is the amount of energy required to convert 1 kg of ice at 0°C into 1 kg of water at 0°C. Therefore, the energy required to melt 1 kg of ice is:
Q2 = mass × latent heat of fusion Q2 = 1 kg × 334 kJ/kg Q2 = 334 kJ
- Heating the water from its boiling point (100°C) to its boiling point: The specific heat capacity of water is approximately 4.18 kJ/kg°C. The initial temperature is 0°C (after melting) and the boiling point of water is 100°C. Therefore, the energy required to heat 1 kg of water from 0°C to 100°C is:
Q3 = mass × specific heat capacity × temperature difference Q3 = 1 kg × 4.18 kJ/kg°C × (100°C - 0°C) Q3 = 418 kJ
- Vaporizing the water into steam: The latent heat of vaporization for water is approximately 2260 kJ/kg. This is the amount of energy required to convert 1 kg of water at its boiling point (100°C) into 1 kg of steam at the same temperature. Therefore, the energy required to vaporize 1 kg of water is:
Q4 = mass × latent heat of vaporization Q4 = 1 kg × 2260 kJ/kg Q4 = 2260 kJ
To calculate the total energy required, we sum up the energy values obtained from each step:
Total energy = Q1 + Q2 + Q3 + Q4 Total energy = 0 kJ + 334 kJ + 418 kJ + 2260 kJ Total energy = 3012 kJ
Since energy is conserved, the energy required to heat the steam is equal to the energy transferred from the steam. The specific enthalpy of steam at 100°C is approximately 2676 kJ/kg (enthalpy at 100°C with respect to ice at 0°C). Therefore, the mass of steam required can be calculated as:
Mass of steam = Total energy / specific enthalpy of steam Mass of steam = 3012 kJ / 2676 kJ/kg Mass of steam ≈ 1.125 kg
Therefore, approximately 1.125 kg of steam at 100°C is required to heat 1 kg of ice until it boils.