To calculate the amount of heat energy required to change a substance through multiple phases, we need to consider the specific heat capacities and phase change enthalpies of the substance.
For ice, we have the following values:
- Specific heat capacity of ice: 2.09 J/g°C
- Heat of fusion (enthalpy of melting) for ice: 334 J/g
For water, we have:
- Specific heat capacity of water: 4.18 J/g°C
- Heat of vaporization (enthalpy of vaporization) for water: 2260 J/g
For steam, we have:
- Specific heat capacity of steam: 2.03 J/g°C
Let's break down the process step by step:
Heating the ice from -10°C to 0°C: Heat energy = mass × specific heat capacity × temperature change Heat energy = 40 g × 2.09 J/g°C × (0°C - (-10°C)) Heat energy = 40 g × 2.09 J/g°C × 10°C Heat energy = 836 J
Melting the ice at 0°C: Heat energy = mass × heat of fusion Heat energy = 40 g × 334 J/g Heat energy = 13,360 J
Heating the water from 0°C to 100°C: Heat energy = mass × specific heat capacity × temperature change Heat energy = 40 g × 4.18 J/g°C × (100°C - 0°C) Heat energy = 16,720 J
Vaporizing the water at 100°C: Heat energy = mass × heat of vaporization Heat energy = 40 g × 2260 J/g Heat energy = 90,400 J
Heating the steam from 100°C to 110°C: Heat energy = mass × specific heat capacity × temperature change Heat energy = 40 g × 2.03 J/g°C × (110°C - 100°C) Heat energy = 8,120 J
Adding up all the individual energy contributions:
Total heat energy = 836 J + 13,360 J + 16,720 J + 90,400 J + 8,120 J Total heat energy = 129,436 J
Therefore, approximately 129,436 J (or 129.4 kJ) of heat energy is required to change a 40 g ice cube from a solid at -10°C to steam at 110°C.