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.
Calculate the total energy required to evaporate completely 1kg of ice that is initially -10°c
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