A thermally isolated vessel contains `100g` of water at `0^(@)C`. When air above the water is pumped out, some of the water freezes and some evaporates at `0^(@)C` itself. Calculate the mass of the ice formed such that no water is left in the vessel. Latent heat of vaporization of water at `0^(@)C=2.10xx10^(6)J//kg` and latent heat of fusion of ice `=3.36xx10^(5)J//kg`.

Explanation

To solve the problem step by step, we will use the principles of thermodynamics, particularly the concept of conservation of energy in a thermally isolated system.

### Step 1: Understand the system
We have a thermally isolated vessel containing 100 g of water at 0°C. When air is pumped out, some water freezes and some evaporates. Our goal is to find the mass of ice formed such that no water is left in the vessel.

### Step 2: Define variables
Let:
- \( y \) = mass of ice formed (in kg)
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