The gross energy requirement, to reduce a very large feed of coal to such a size that $80 \%$ of the product passes through a $100 ~\mu \mathrm{m}$ screen, is $13 \text{kWh}$ per ton of feed. In a process, $250$ tons $\mathrm{h}^{-1}$ of coal is crushed. The range of feed sizes is such that $80 \%$ of the feed passes through an opening of $100 \text{ mm}$. The product size range is to be such that $80 \%$ of the product passes through an opening of $25 \text{ mm}.$ According to the Bond's law, which one of the following is the power consumption (in $\text{kW}$)?
- $12.8$
- $25.7$
- $51.4$
- $102.7$
