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Question

A thermally insulated vessel contains some water at 0∘C. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given that the latent heat of vaporization of water at 0∘C is 21×105 J/kg and latent heat of freezing of water at 0∘C is 3.36×105 J/kg. The maximum percentage of water vapour that will be solidified in this manner will be -

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Solution

The correct option is **A** 86.2 %

As the system is thermally isolated, the heat required for vaporization is extracted from the water itself. Since the water in the vessel is at 0∘C, this results in part of the water getting frozen. Since the vapor is pumped out, the process will continue till all the remaining water is converted into ice.

Let x be the maximum fraction of water that solidifies and (1−x) is the fraction that gets vaporized.

By using,

miLf=mslv at 0∘C, we can say that,

x×3.36×105=(1−x)×21×105

⇒3.36x+21x=21

or x=0.862 or 86.2 %

Thus, option (a) is the correct answer.

As the system is thermally isolated, the heat required for vaporization is extracted from the water itself. Since the water in the vessel is at 0∘C, this results in part of the water getting frozen. Since the vapor is pumped out, the process will continue till all the remaining water is converted into ice.

Let x be the maximum fraction of water that solidifies and (1−x) is the fraction that gets vaporized.

By using,

miLf=mslv at 0∘C, we can say that,

x×3.36×105=(1−x)×21×105

⇒3.36x+21x=21

or x=0.862 or 86.2 %

Thus, option (a) is the correct answer.

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