7. 7. How much heat energy is needed to convert 1 kg of ice at \( 0^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \) ? 8. 8. How much heat eneray is needed to comnletely convert 60

To calculate the heat energy needed to convert 1 kg of ice at \( 0^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \), we need to consider the following steps: 1. **Melting the ice**: The heat energy required to melt 1 kg of ice at \( 0^{\circ} \mathrm{C} \) to water at \( 0^{\circ} \mathrm{C} \) is known as the latent heat of fusion of ice. The latent heat of fusion of ice is approximately \( 334 \, \text{kJ/kg} \). 2. **Raising the temperature of water**: The heat energy required to raise the temperature of 1 kg of water from \( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \) is calculated using the specific heat capacity of water, which is approximately \( 4.18 \, \text{kJ/(kg·°C)} \). 3. **Vaporizing the water**: The heat energy required to vaporize 1 kg of water at \( 100^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \) is known as the latent heat of vaporization of water. The latent heat of vaporization of water is approximately \( 2260 \, \text{kJ/kg} \). Therefore, the total heat energy required to convert 1 kg of ice at \( 0^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \) is the sum of the heat energy required for each step. Let's calculate the total heat energy required. Calculate the value by following steps: - step0: Calculate: \(334+4.18\times 100+2260\) - step1: Multiply the numbers: \(334+418+2260\) - step2: Add the numbers: \(3012\) The total heat energy needed to convert 1 kg of ice at \( 0^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \) is 3012 kJ.