Reactor Power Calculation

Multiplying the reaction rate per unit volume by the total volume of the core results in the total number of reactions occurring in the core per unit time. If the amount of energy involved in each reaction were known, it would be possible to determine the rate of energy release (power) due to a certain reaction.
In a reactor where the average energy per fission is 200 MeV, it is possible to determine the number of fissions per second that are necessary to produce one watt of power using the following conversion factors.

1 fission = 200 MeV
1 MeV = 1.602 x 10^-6 ergs
1 erg = 1 x 10^-7 watt-sec

This is equivalent to stating that 3.12 x 10¹⁰ fissions release 1 watt-second of energy.

Multiplying the reaction rate by the volume of the reactor results in the total fission rate for the entire reactor. Dividing by the number of fissions per watt-sec results in the power released by fission in the reactor in units of watts. This relationship is shown mathematically in Equation (1-1) below.

(1-1)

where:

P = power (watts)
Φ_th = thermal neutron flux (neutrons/cm2 -sec)
Σ_f = macroscopic cross section for fission (cm-1 )
V = volume of core (cm3)