For the reaction of one mole of zinc dust with one mole of sulphuric acid in a bomb calorimeter, $\Delta U$ and $w$ corresponds to:

A bomb calorimeter is a constant volume device ($V=\text{constant}$), so $dV=0$.Work done, $w=-P\Delta V=0$.From the first law of thermodynamics, $\Delta U=q+w$. Since $w=0$, $\Delta U=q_v$.The reaction of $\text{Zn}$ with ${\text{H}}_2{\text{SO}}_4$ is exothermic, meaning heat is released ($q<0$).Therefore, $\Delta U<0$ and $w=0$.