According to the First Law of Thermodynamics, the change in internal energy ($\Delta U$) is given by: $\Delta Q = \Delta U + \Delta W \implies \Delta U = \Delta Q - \Delta W$

1. Calculate Heat Absorbed ($\Delta Q$): The heat absorbed during the phase change is determined by the specific latent heat of vaporization ($L$) and the mass ($m$). $\Delta Q = m \times L$ $\Delta Q = 1 \text{ g} \times 2256 \text{ J/g} = 2256 \text{ J}$

2. Calculate Work Done ($\Delta W$): Work done during expansion at constant pressure is given by $\Delta W = P\Delta V$. Pressure ($P$) = $1 \times 10^5 \text{ Pa}$ Change in volume ($\Delta V$) = $V_{\text{steam}} - V_{\text{water}} = 1671 \text{ cm}^3 - 1 \text{ cm}^3 = 1670 \text{ cm}^3$

• Convert $\Delta V$ to SI units ($\\text{m}^3$): $1670 \times 10^{-6} \text{ m}^3$

$\Delta W = (1 \times 10^5 \text{ Pa}) \times (1670 \times 10^{-6} \text{ m}^3) = 167 \text{ J}$

3. Calculate Internal Energy Change ($\Delta U$): $\Delta U = 2256 \text{ J} - 167 \text{ J} = 2089 \text{ J}$