Calculate the masses ${?}^{233}U$ and ${?}^{238}U$ per metric ton $(t)$ of

uranium ore, assuming the total is $0\mathrm{.}25wt\%$ of the ore. $10.$ Coal has a heat content of $19-28G\frac{J}{t}$ of mined material. Uranium as employed in an LWR has a heat content of $460G\frac{J}{k}g$ of natural uranium metal.

a$.$ Calculate the heat content of a tone of low$-$assay uranium ore and its ratio to that of the extreme coal value.

b$.$ Considering the electrical conversion of efficiencies $($MWe$/$MWth$)$ are about $32\%$ and $38\%$ respectively for LWR and coal plant, calculate the electric energy ratios per ton of mined ore.

The ${?}^{233}U$ and the ${?}^{238}U$ masses in natural uranium are split between enriched and depleted streams as a result of the enrichment process. If the input masses and the output enrichments are specified, mass conversion determines the maximum $($no loss$)$ quantity of each isotope in the output streams. Considering a $1kg$ input of natural uranium, a $3$ wt $\%{?}^{233}U$ enriched stream, and a $0\mathrm{.}3wt\%{?}^{23}U$ depleted stream:

a$.$ Calculate the masses of ${?}^{23}U,{?}^{238}U,$ and the total $U$ in each of the two output streams.

b$.$ Calculate the fraction of the initial ${?}^{233}U$ that ends up in each output stream.

c$.$ Repeat part $($b$)$ for the ${?}^{23}U$ and total $U.$