Answer:
To calculate the energy needed to drop the temperature of a substance, we need to consider the energy changes that occur during each segment of the temperature change: solid to liquid, liquid to gas, solid to liquid at the freezing point, liquid to solid at the freezing point, and gas to liquid at the boiling point.
Segment 1: Heating the substance from 225°C to the melting point (35.5°C)
The energy required for this segment can be calculated using the specific heat of the solid:
Energy = mass × specific heat × temperature change
Energy = 87.3 g × 4.76 J/g°C × (35.5°C - 225°C)
Segment 2: Melting the substance at the freezing point (35.5°C)
The energy required for this segment is the heat of fusion multiplied by the mass of the substance:
Energy = mass × heat of fusion
Energy = 87.3 g × 68.1 J/g
Segment 3: Heating the substance from the melting point (35.5°C) to the boiling point (165.5°C)
The energy required for this segment can be calculated using the specific heat of the liquid:
Energy = mass × specific heat × temperature change
Energy = 87.3 g × 3.54 J/g°C × (165.5°C - 35.5°C)
Segment 4: Vaporizing the substance at the boiling point (165.5°C)
The energy required for this segment is the heat of vaporization multiplied by the mass of the substance:
Energy = mass × heat of vaporization
Energy = 87.3 g × 193.8 J/g
Segment 5: Cooling the substance from the boiling point (165.5°C) to the final temperature (1.75°C)
The energy required for this segment can be calculated using the specific heat of the liquid:
Energy = mass × specific heat × temperature change
Energy = 87.3 g × 3.54 J/g°C × (1.75°C - 165.5°C)
To find the total energy required, sum up the energies from all segments:
Total energy = Energy segment 1 + Energy segment 2 + Energy segment 3 + Energy segment 4 + Energy segment 5
Simply substitute the values and perform the calculations to find the total energy required.