Question

Suppose India had a targe of producing by $$2020AD$$, $$200,000MW$$ of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (ie conversion to electric energy) of thermal energy produced in a reactor was $$25$$%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of $$^{ 235 }{ U }$$ to be about $$200MeV$$

Answer 1

Energy released per fission $$=200MeV$$
Efficiency of utilization $$=25$$%
Electrical energy produced per fission
$$=\cfrac{25}{100}\times 200=50MeV$$
$$=50\times 1.6\times {10}^{-13}=8\times {10}^{-12}J$$
Targe of electric power $$=200,000MW$$
Electric power to be obtained from nuclear plants
$$\cfrac{10}{100}\times 2000000=20,000MW=2\times {10}^{10}J{s}^{-1}$$
Number of fission reactions required per year
$$=\cfrac{{10}^{10}\times 60\times 60\times 24\times 365}{8\times {10}^{-12}}=3.942\times {10}^{28}$$
Mass of $$^{ 235 }{ U }$$ needed per year
$$=\cfrac{235}{6.023\times {10}^{23}}\times 7.884\times {10}^{28}$$
$$=3.076\times {10}^{7}g=3.076\times {10}^{4}kg$$