Calculate the thermal energy required to convert 5kg of ice at 0 Celsius to steam at 100 Celsius
To calculate the thermal energy required to convert a substance from one phase to another, you need to consider the heat required for each phase transition.
First, we need to calculate the energy required to raise the temperature of the ice from 0°C to its melting point:
Q1 = m * c * ΔT1
Where:
Q1 = thermal energy
m = mass (5 kg)
c = specific heat capacity of ice (2.09 J/g°C or 2090 J/kg°C)
ΔT1 = change in temperature (0°C - (-10°C) = 10°C)
Q1 = 5 kg * 2090 J/kg°C * 10°C
Q1 = 104500 J
Next, we need to calculate the thermal energy required to convert the ice to water at 0°C:
Q2 = m * ΔHf
Where:
Q2 = thermal energy
m = mass (5 kg)
ΔHf = heat of fusion for ice (334,000 J/kg)
Q2 = 5 kg * 334,000 J/kg
Q2 = 1,670,000 J
Now, we need to calculate the thermal energy required to raise the temperature of the water from 0°C to its boiling point:
Q3 = m * c * ΔT2
Where:
Q3 = thermal energy
m = mass (5 kg)
c = specific heat capacity of water (4.18 J/g°C or 4180 J/kg°C)
ΔT2 = change in temperature (100°C - 0°C = 100°C)
Q3 = 5 kg * 4180 J/kg°C * 100°C
Q3 = 2,090,000 J
Finally, we need to calculate the thermal energy required to convert the water to steam at 100°C:
Q4 = m * ΔHv
Where:
Q4 = thermal energy
m = mass (5 kg)
ΔHv = heat of vaporization for water (2,260,000 J/kg)
Q4 = 5 kg * 2,260,000 J/kg
Q4 = 11,300,000 J
Now we can find the total thermal energy required:
Total Thermal Energy = Q1 + Q2 + Q3 + Q4
Total Thermal Energy = 104500 J + 1670000 J + 2090000 J + 11300000 J
Total Thermal Energy = 15,940,500 J
Therefore, the thermal energy required to convert 5 kg of ice at 0°C to steam at 100°C is 15,940,500 J.
To calculate the thermal energy required to convert 5kg of ice at 0 degrees Celsius to steam at 100 degrees Celsius, you would need to take into account the different phases involved.
The process consists of three main steps:
1. Heating the ice from 0 degrees Celsius to its melting point.
2. Melting the ice into water at 0 degrees Celsius.
3. Heating the water from 0 degrees Celsius to its boiling point and converting it to steam.
Each step requires a specific amount of energy, which can be calculated using the following formulas:
1. Heating ice: Q1 = m * c * ΔT
- m is the mass of the ice (5kg in this case).
- c is the specific heat capacity of ice (approximately 2,090 J/kg·°C).
- ΔT is the change in temperature (0°C - (-273.15°C) = 273.15°C).
2. Melting ice: Q2 = m * Lf
- m is the mass of the ice (5kg).
- Lf is the latent heat of fusion for water (approximately 333,500 J/kg).
3. Heating water: Q3 = m * c * ΔT
- m is the mass of the water (5kg).
- c is the specific heat capacity of water (approximately 4,186 J/kg·°C).
- ΔT is the change in temperature (100°C - 0°C = 100°C).
To find the total thermal energy required, you add up the values from each step:
Total thermal energy = Q1 + Q2 + Q3
Let's calculate the values for each step:
Q1 = (5kg) * (2,090 J/kg·°C) * (273.15°C) = 2,267,442.5 J
Q2 = (5kg) * (333,500 J/kg) = 1,667,500 J
Q3 = (5kg) * (4,186 J/kg·°C) * (100°C) = 2,093,000 J
Total thermal energy = 2,267,442.5 J + 1,667,500 J + 2,093,000 J = 6,027,942.5 J
Therefore, the thermal energy required to convert 5kg of ice at 0 degrees Celsius to steam at 100 degrees Celsius is approximately 6,027,942.5 Joules.
Melt: mL
Heat to 100 : mc change T
Steam: mL
You'll need to look up heats of fusion and vaporization and specific heat of water.