Final answer:
To convert 0.500 kg of ice at -20°C to steam at 250°C, you would need 20.3 kJ to raise the temperature of the ice, 167 kJ for the phase change from ice to water, and additional energy to raise the temperature of the water from 0°C to 250°C. The exact quantity of energy required would depend on the amount of ice melted and steam formed.
Step-by-step explanation:
To calculate the quantity of energy required to convert 0.500 kg of ice at -20°C to steam at 250°C, we need to consider the energy required for each stage of the phase change. First, we need to raise the temperature of the ice from -20°C to 0°C. The specific heat capacity of ice is 2.03 J/g°C, so the energy required is given by Q = m * c * ΔT, where m is the mass of the ice, c is the specific heat capacity of ice, and ΔT is the change in temperature. Using these values, the energy required to raise the temperature of the ice is:
Q = 0.500 kg * 2.03 J/g°C * (0°C - (-20°C)) = 20.3 kJ
Next, we need to convert the ice at 0°C to water at 0°C. The latent heat of fusion for ice is 334 J/g, so the energy required is given by Q = m * ΔH, where ΔH is the latent heat of fusion. Using these values, the energy required for the phase change is:
Q = 0.500 kg * 334 J/g = 167 kJ
Finally, we need to raise the temperature of the water from 0°C to 100°C, then from 100°C to 250°C. The specific heat capacity of water is 4.18 J/g°C. The energy required for each stage can be calculated using the same formula as before. Adding up all the energies, we get:
Total Energy = 20.3 kJ + 167 kJ + (mass of water) * 4.18 J/g°C * (100°C - 0°C) + (mass of water) * 4.18 J/g°C * (250°C - 100°C)
However, the mass of the water at each stage will vary depending on the amount of ice that has melted and the amount of steam that has formed. Therefore, we would need additional information about the process to determine the exact quantity of energy required.