To determine the amount of heat energy required to convert 10g of ice at 0°C to vapor at 100°C, we need to consider the different phase changes and the specific heat capacities involved.
The energy required can be calculated as follows:
- Heat energy to raise the temperature of the ice from 0°C to its melting point (0°C): Q1 = m * c_ice * ΔT_1
Where: m = mass of ice = 10g c_ice = specific heat capacity of ice = 2.09 J/g°C (approximately) ΔT_1 = change in temperature = 0°C - (-0°C) = 0°C
Q1 = 10g * 2.09 J/g°C * 0°C = 0 Joules (no change in temperature)
- Heat energy to melt the ice at 0°C: Q2 = m * ΔH_fusion
Where: ΔH_fusion = heat of fusion for ice = 334 J/g
Q2 = 10g * 334 J/g = 3340 Joules
- Heat energy to raise the temperature of the water from 0°C to 100°C: Q3 = m * c_water * ΔT_2
Where: c_water = specific heat capacity of water = 4.18 J/g°C (approximately) ΔT_2 = change in temperature = 100°C - 0°C = 100°C
Q3 = 10g * 4.18 J/g°C * 100°C = 4180 Joules
- Heat energy to convert the water at 100°C to vapor at 100°C: Q4 = m * ΔH_vaporization
Where: ΔH_vaporization = heat of vaporization for water = 2260 J/g
Q4 = 10g * 2260 J/g = 22,600 Joules
Finally, we sum up the individual heat energies: Total heat energy = Q1 + Q2 + Q3 + Q4 Total heat energy = 0 Joules + 3340 Joules + 4180 Joules + 22,600 Joules Total heat energy = 30,120 Joules
Therefore, the amount of heat energy required to convert 10g of ice at 0°C to vapor at 100°C is approximately 30,120 Joules.