Suppose India had a target of producing by 2020 AD, 200000 MW of electric power, 10% of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilisation (i.e…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 200 MeV.
Total target power = 200000 = 2 x ${{10}^{5}}$ MW
Total nuclear power = 10% of total target power = 10/100 x 2 x ${{10}^{5}}$ = 2 x ${{10}^{4}}$ MW
Energy produced/fission = 200 MeV
Efficiency of power plant = 25%
Energy converted into electrical energy per fission = 25 /100 x 200 = 50 MeV
= 50 x 1.6 x ${{10}^{-13}}$ J
Total electrical energy to be produced per year = 2 x ${{10}^{4}}$ MW = 2 x ${{10}^{4}}$ x ${{10}^{6}}$ W = 2 x ${{10}^{10}}$ W
=2 x ${{10}^{10}}$ J/s = 2 x ${{10}^{10}}$ x 60 x 60x24x365 J/yr
Number of fission in one year,
n = 2 x ${{10}^{10}}$ x 60x60x24x365/ 50x1.6x${{10}^{-13}}$
n = 2 x 36x24x365/8 x ${{10}^{24}}$
Mass of 6.023x${{10}^{23}}$ atoms =235 x ${{10}^{-3}}$ kg
The mass of uranium needed per year is 3.08 x ${{10}^{4}}$kg