`1gm` water at `100^(@)C` is heated to convert into steam at `100^(@)C` at `1atm`. Find out chage in internal energy of water. It is given that volume of `1gm` water at `100^(@)C = 1c c`, volume of `1gm` steam at `100^(@)C = 167 1 c c`. Latent heat of vaporization `= 540 cal//g`. (Mechanical equivalent of heat `J = 4.2J//cal)`

Explanation

To find the change in internal energy of water when 1 gm of water at \(100^\circ C\) is converted into steam at \(100^\circ C\) at 1 atm, we will follow these steps:

### Step 1: Understand the Problem
We need to find the change in internal energy (\(\Delta U\)) when 1 gm of water is converted to steam at the same temperature. We know the latent heat of vaporization and the volumes of water and steam.

### Step 2: Calculate the Heat Added (\(\Delta Q\))
The heat added to convert water to steam is given by the latent heat of vaporization. For 1 gm of water:
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