For the reaction of one mole zine dust with one mole sulphuric acid in a bomb calorimeter, $\Delta \mathrm{U}$ and $\mathrm{w}$ correspond to

$\mathrm{Zn}+{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{ZnSO}}_4+{\mathrm{H}}_2$

In a bomb calorimeter, there is no expansion in volume, so, the work done will be zero.

This reaction is exothermic. So, some heat will be evolved which will result in a lowering of internal energy.

$\text{ Hence, }\Delta \mathrm{U}<0, \mathrm{W}=0\text{. }$