Calculate the work done (w) and internal energy change (`DeltaU`), when one mole of water at `100^@C` vaporises against an atmospheric pressure of 1 atm assuming ideal gas behaviour. Heat of vapourisation of water at `100^@C` is `1020 cal mol^(-1)`.

Explanation

To solve the problem of calculating the work done (w) and the change in internal energy (ΔU) when one mole of water at 100°C vaporizes against an atmospheric pressure of 1 atm, we can follow these steps:

### Step 1: Identify the Given Data
- Heat of vaporization of water at 100°C, \( Q = 1020 \, \text{cal/mol} \)
- Atmospheric pressure, \( P_{\text{external}} = 1 \, \text{atm} \)
- Volume of 1 mole of liquid water, \( V_1 = 18 \, \text{mL} = 18 \times 10^{-3} \, \text{L} \)

### Step 2: Calculate the Volume of Vapor (Steam)
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