Work is done against atmospheric pressure which is given as $P_{0}$

since the densities of water and steam at $100^{\circ} \mathrm{C}$ are given as $p_{1}$ and $p_{2}$ respectively.

$d W=P_{0}\left(V_{2}-V_{1}\right)=P_{0}\left(\frac{m}{p_{2}}-\frac{m}{p_{1}}\right)=P_{0} \times 1\left(\frac{1}{p_{2}}-\frac{1}{p_{1}}\right)$ since $m=1$ as given.

$\therefore d U=Q-P_{0} \times 1\left(\frac{1}{p_{2}}-\frac{1}{p_{1}}\right)=Q+P_{0}\left(\frac{1}{p_{1}}-\frac{1}{p_{2}}\right)$