Calculate w and `DeltaU` for the conversion of 1 mol of water at `100^(@)C` to steam at 1 atm pressure.Heat of vaporisation of water at `100^(@)C` is 40.670 kJ `mol^(-1)`.Assume ideal gas behaviour.

Explanation

To solve the problem of calculating the work (w) and change in internal energy (ΔU) for the conversion of 1 mole of water at 100°C to steam at 1 atm pressure, we can follow these steps:

### Step 1: Understand the process
The conversion of water to steam at 100°C involves a phase change from liquid to gas (vaporization). The heat of vaporization (ΔH_vap) is given as 40.670 kJ/mol.

### Step 2: Calculate the work done (w)
For an ideal gas undergoing expansion against a constant external pressure, the work done can be calculated using the formula:
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