A thermal 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 latent heat of vaporization of water at `0^(@)C = 21 xx 10^(5) J//kg` and latent heat of freezing of water `=3.36 xx 10^(5) J//kg`. the maximum percentage amount of water vapour that will be solidified in this manner will be:

Options

A. `86.2%`
B. `33.6%`
C. `21%`
D. `24.36%`

Answer

A

Explanation

As the system is thermally isolated, the heat required for vaporization is extracted from water itself. The water in the vessel being at `0^(@)C` results in part of water getting frozen. Let `x` be the maximum fraction of water in this way. The `(1-x)` is the fraction that gets vaporized.
`:. x xx 3.36xx10^(5) = (1-x)xx21xx10^(5)`
or `x=0.862`.