To determine the amount of steam at 150 °C needed to melt 1 kg of ice at 0 °C, we need to consider the energy required for each phase change and the temperature difference.
- 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
To calculate the amount of steam required, we need to find out how much heat the steam can transfer to the ice to provide the necessary energy. The specific enthalpy of steam at 150 °C is approximately 2766 kJ/kg (enthalpy at 150 °C with respect to ice at 0 °C).
The heat transferred from the steam to melt the ice can be calculated using:
Q2 = mass of steam × specific enthalpy of steam
Rearranging the equation, we can solve for the mass of steam:
mass of steam = Q2 / specific enthalpy of steam mass of steam = 334 kJ / 2766 kJ/kg mass of steam ≈ 0.1206 kg (or 120.6 grams)
Therefore, approximately 120.6 grams of steam at 150 °C is needed to melt 1 kg of ice at 0 °C.