Calculate the total energy required to evaporate completely 1kg of ice that is initially -10°c
To calculate the total energy required to evaporate completely 1 kg of ice, we need to consider the energy required to heat up the ice to its melting point and then the energy required to change the state of the ice from solid to liquid (latent heat of fusion), and finally the energy required to raise the temperature of the water from its melting point to its boiling point and then the energy required to change the state of water from liquid to vapor (latent heat of vaporization).
First, let's calculate the energy required to heat the ice from -10°C to 0°C:
Energy = m * c * ΔT
m = mass of ice = 1 kg
c = specific heat capacity of ice = 2.09 kJ/kg°C
ΔT = change in temperature = 0°C - (-10°C) = 10°C
Energy = 1 kg * 2.09 kJ/kg°C * 10°C
Energy = 20.9 kJ
Next, let's calculate the energy required to change the state of the ice from solid to liquid:
Energy = m * Lf
Lf = latent heat of fusion of ice = 334 kJ/kg
Energy = 1 kg * 334 kJ/kg
Energy = 334 kJ
Now, let's calculate the energy required to heat the water from 0°C to 100°C:
Energy = m * c * ΔT
m = mass of water = 1 kg
c = specific heat capacity of water = 4.18 kJ/kg°C
ΔT = change in temperature = 100°C - 0°C = 100°C
Energy = 1 kg * 4.18 kJ/kg°C * 100°C
Energy = 418 kJ
Finally, let's calculate the energy required to change the state of water from liquid to vapor:
Energy = m * Lv
Lv = latent heat of vaporization of water = 2260 kJ/kg
Energy = 1 kg * 2260 kJ/kg
Energy = 2260 kJ
Now, we can add up all the energies:
Total Energy = Energy to heat up ice + Energy to change ice to water + Energy to heat up water + Energy to change water to vapor
Total Energy = 20.9 kJ + 334 kJ + 418 kJ + 2260 kJ
Total Energy = 3032.9 kJ
Therefore, the total energy required to completely evaporate 1 kg of ice that is initially -10°C is approximately 3032.9 kJ.
To calculate the total energy required to evaporate 1 kg of ice, we need to go through several steps:
Step 1: Calculate the energy required to bring the ice to its melting point.
The specific heat capacity of ice is 2.09 kJ/kg°C, which means it takes 2.09 kJ of energy to raise the temperature of 1 kg of ice by 1°C.
The ice is initially at -10°C, so we need to bring it up to its melting point, which is 0°C.
Energy required = mass × specific heat capacity × change in temperature
= 1 kg × 2.09 kJ/kg°C × (0°C - (-10°C))
= 1 kg × 2.09 kJ/kg°C × 10°C
= 20.9 kJ
Step 2: Calculate the energy required to melt the ice.
The specific latent heat of fusion of ice is 334 kJ/kg, which means it takes 334 kJ of energy to change 1 kg of ice at its melting point into water at the same temperature.
Energy required = mass × specific latent heat of fusion
= 1 kg × 334 kJ/kg
= 334 kJ
Step 3: Calculate the energy required to heat the water from 0°C to its boiling point.
The specific heat capacity of water is 4.18 kJ/kg°C, which means it takes 4.18 kJ of energy to raise the temperature of 1 kg of water by 1°C.
The water is at 0°C, and we need to bring it up to its boiling point, which is 100°C.
Energy required = mass × specific heat capacity × change in temperature
= 1 kg × 4.18 kJ/kg°C × (100°C - 0°C)
= 1 kg × 4.18 kJ/kg°C × 100°C
= 418 kJ
Step 4: Calculate the energy required to vaporize the water.
The specific latent heat of vaporization of water is 2260 kJ/kg, which means it takes 2260 kJ of energy to convert 1 kg of water at its boiling point into steam at the same temperature.
Energy required = mass × specific latent heat of vaporization
= 1 kg × 2260 kJ/kg
= 2260 kJ
Step 5: Calculate the total energy required.
Total energy required = energy to bring ice to its melting point + energy to melt the ice + energy to bring water to its boiling point + energy to vaporize the water
= 20.9 kJ + 334 kJ + 418 kJ + 2260 kJ
= 3032.9 kJ
Therefore, the total energy required to evaporate completely 1 kg of ice that is initially at -10°C is 3032.9 kJ.