 # Suppose India had a target of producing by 2020 AD, 200000 MW of electric power

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