Answer:
To calculate the energy required to raise the temperature of ice, we need to go through several steps. Let's break it down:
Step 1: Determine the energy required to heat ice from -33 °C to 0 °C
The specific heat capacity of ice (solid) is 2.09 J/(g·°C).
First, let's calculate the energy required to bring the ice from -33 °C to 0 °C:
Energy = mass × specific heat capacity × temperature change
= 14.3 g × 2.09 J/(g·°C) × (0 °C - (-33 °C))
Since the temperature change is from a negative value to a positive value, the absolute value of the temperature change is necessary:
Energy = 14.3 g × 2.09 J/(g·°C) × (0 °C - (-33 °C))
= 14.3 g × 2.09 J/(g·°C) × 33 °C
= 14.3 g × 2.09 J/(g·°C) × 33 °C
= 14.3 g × 2.09 J/(g·°C) × 33 °C
Calculating this gives us:
Energy = 998.847 kJ (rounded to three decimal places)
Step 2: Determine the energy required to melt ice into water
The amount of energy required to melt ice into water is known as the heat of fusion. The heat of fusion for ice is 334 J/g.
Since the mass of the ice remains constant (14.3 g), we can calculate the energy required to melt the ice:
Energy = mass × heat of fusion
= 14.3 g × 334 J/g
Calculating this gives us:
Energy = 4776.2 J (rounded to three decimal places)
Energy = 4.776 kJ (rounded to three decimal places)
Step 3: Determine the energy required to heat water from 0 °C to 100 °C
The specific heat capacity of water (liquid) is 4.18 J/(g·°C).
We need to calculate the energy required to heat the water from 0 °C to 100 °C:
Energy = mass × specific heat capacity × temperature change
= 14.3 g × 4.18 J/(g·°C) × (100 °C - 0 °C)
Calculating this gives us:
Energy = 5941.94 kJ (rounded to three decimal places)
Step 4: Determine the energy required to heat water vapor (steam) from 100 °C to 109 °C
The specific heat capacity of water vapor (gas) is 2.03 J/(g·°C).
Let's calculate the energy required to heat the water vapor (steam) from 100 °C to 109 °C:
Energy = mass × specific heat capacity × temperature change
= 14.3 g × 2.03 J/(g·°C) × (109 °C - 100 °C)
Calculating this gives us:
Energy = 209.483 kJ (rounded to three decimal places)
Step 5: Sum up the energies from all steps
To find the total energy required, we need to sum up the energies obtained from each of the steps:
Total energy = Energy from step 1 + Energy from step 2 + Energy from step 3 + Energy from step 4
= 998.847 kJ + 4.776 kJ + 5941.94 kJ + 209.483 kJ
Calculating this gives us:
Total energy = 7164.046 kJ (rounded to three decimal places)
Thus, the total energy required to raise the temperature of 14.3 g of ice from -33 °C to 109 °C is approximately 7164.046 kJ.
