How much energy is needed to convert 10kg of ice at -15 degrees centigrade to 125 degrees centigrade of steam?
Express your answer in joules.
To calculate the energy needed to convert ice at -15 degrees Celsius to steam at 125 degrees Celsius, we need to consider two main steps:
1. Heating the ice from -15 degrees Celsius to its melting point (0 degrees Celsius).
2. Melting the ice at 0 degrees Celsius and heating the resulting water from 0 degrees Celsius to its boiling point (100 degrees Celsius).
3. Finally, vaporizing the water at its boiling point and heating it to the final temperature of 125 degrees Celsius.
We can break down the process into three parts and calculate the energy required for each step using the specific heat capacity and the latent heat of fusion/evaporation:
1. Heating the ice from -15 degrees Celsius to 0 degrees Celsius:
The specific heat capacity of ice is 2.1 J/g°C. So, to calculate the energy required, we need to determine the temperature change and the mass of the ice.
Temperature change = 0°C - (-15°C) = 15°C
Mass of ice = 10 kg = 10,000 g
Energy (Q1) = mass × specific heat capacity × temperature change
Q1 = 10,000 g × 2.1 J/g°C × 15°C = 315,000 J
2. Melting the ice at 0 degrees Celsius:
The latent heat of fusion is the energy required to transform a substance from a solid to a liquid state. For water, it is 334 J/g.
Energy (Q2) = mass × latent heat of fusion
Q2 = 10,000 g × 334 J/g = 3,340,000 J
3. Heating the resulting water from 0 degrees Celsius to 100 degrees Celsius:
The specific heat capacity of water is 4.18 J/g°C.
Temperature change = 100°C - 0°C = 100°C
Mass of water = mass of ice (10,000 g)
Energy (Q3) = mass × specific heat capacity × temperature change
Q3 = 10,000 g × 4.18 J/g°C × 100°C = 4,180,000 J
4. Vaporizing the water at its boiling point and heating it to 125 degrees Celsius:
The latent heat of vaporization is the energy required to transform a substance from a liquid to a gas state. For water, it is 2260 J/g.
Energy (Q4) = mass × latent heat of vaporization
Q4 = 10,000 g × 2260 J/g = 22,600,000 J
Now, we can calculate the total energy required by summing up the energies from each step:
Total energy = Q1 + Q2 + Q3 + Q4
Total energy = 315,000 J + 3,340,000 J + 4,180,000 J + 22,600,000 J
Total energy = 30,435,000 J
Therefore, approximately 30,435,000 joules of energy are needed to convert 10 kg of ice at -15 degrees Celsius to steam at 125 degrees Celsius.