To solve this problem, we need to calculate the change in internal energy of the water as it converts to steam.$\\$Given:$\\$• Mass of water $= 0.1$ g$\\$• Heat energy supplied $= 54$ cal$\\$• Volume of steam produced $= 167.1$ cc$\\$• Pressure $= 1.013 \times 10^5$ N/m$^2 \\$First, convert the heat energy from calories to joules:$\\ 1$ cal$= 4.184$ J$\\ 54$ cal$= 54 \times 4.184$ J$= 225.936$ J$\\$The work done $(W)$ by the system during the expansion can be calculated using the formula:$\\ W = P \Delta V \\$Convert the volume from cc to $m^3: \\ 167.1$ cc$= 167.1 \times 10^{-6}$ m$^3 \\$Substitute the values into the work formula:$\\ W = 1.013 \times 10^5 \times 167.1 \times 10^{-6} \\ W = 16.923$ J$\\$The change in internal energy $(\Delta U)$ is given by the first law of thermodynamics:$\\ \Delta U = Q - W \\$Substitute the values for $Q$ and $W: \\ \Delta U = 225.936 - 16.923 \\ \Delta U = 209.013$ J$\\$Rounding to the nearest tenth, the change in internal energy is approximately $208.7$ J.$\\$Therefore, the correct option is 2: $208.7$ J.