A thermally insulated vessel contains some water at 0 degree celsius ....
Introduction:
In this scenario, we have a thermally insulated vessel containing water at 0 degrees Celsius. The vessel is connected to a vacuum pump to remove water vapor, resulting in the freezing of some water. We are given the latent heat of vaporization of water at 0 degrees Celsius and the latent heat of freezing of water.
Calculation of Maximum Percentage of Water Solidified:
To determine the maximum percentage of water solidified, we need to compare the energy required for vaporization and freezing.
1. Energy Required for Vaporization:
The latent heat of vaporization of water at 0 degrees Celsius is given as 21 × 10^5 J/kg. This means that to convert 1 kg of water at 0 degrees Celsius into water vapor at the same temperature, 21 × 10^5 J of energy is required.
2. Energy Released during Freezing:
The latent heat of freezing of water is given as 3.36 × 10^5 J/kg. This means that when 1 kg of water at 0 degrees Celsius freezes, it releases 3.36 × 10^5 J of energy.
3. Comparison and Calculation:
To find the maximum percentage of water solidified, we compare the energy required for vaporization and the energy released during freezing.
Let's assume we have 1 kg of water in the vessel.
a. Energy Required for Vaporization:
To convert 1 kg of water into water vapor, we need 21 × 10^5 J of energy.
b. Energy Released during Freezing:
When 1 kg of water freezes, it releases 3.36 × 10^5 J of energy.
c. Net Energy:
The net energy required to convert 1 kg of water into water vapor and then freeze it is given by the difference between the energy required for vaporization and the energy released during freezing:
Net Energy = Energy required for vaporization - Energy released during freezing
Net Energy = (21 × 10^5) - (3.36 × 10^5)
Net Energy = 17.64 × 10^5 J
d. Maximum Percentage of Water Solidified:
To find the maximum percentage of water solidified, we divide the energy released during freezing by the net energy and multiply by 100:
Maximum Percentage of Water Solidified = (Energy released during freezing / Net Energy) * 100
Maximum Percentage of Water Solidified = (3.36 × 10^5 / 17.64 × 10^5) * 100
Maximum Percentage of Water Solidified ≈ 19.05%
Conclusion:
In this scenario, the maximum percentage of water that will be solidified is approximately 19.05%. This is calculated by comparing the energy required for vaporization and the energy released during freezing. The net energy required to convert water into vapor and then freeze it is determined, and the percentage of water solidified is calculated based on this net energy.
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