A typical nuclear fission power plant produces approximately

A typical nuclear fission power plant produces approximately 0.96 GW of electrical power. Assume the plant has an overall efficiency of 44.4% and each fission produces 200 MeV of energy. Calculate the mass of ^235U consumed each day.

Solution

Produced in one day = E = P.t =( 0.96 * 10^9 J/s ) * (24 * 3600) s/day = 8.29 * 10 ^ 13 J

At 44.4 % efficiency , need from reactions = E\' = E/0,444 = 1.86 * 10^ 14 J

Per reaction Q = 200Mev * 1.6 * 10^ -19 J/eV = 3.2 * 10^ -11

Therefore no. of reactions = N = E\' /Q = 1.86 * 10^ 14 J / 3.2 * 10^ -11 = 5.81 * 10^ 24 reactions

mass consumed = N * m_u = 5.81 * 10^ 24 * 235u * 1.66 * 10^-27

= 2.26 Kg