## A Rough Model of a Nuclear Reactor

This model is very rough however it gives some idea about power and energy output from a nuclear reactor which I will use in later posts. The model is very simplistic but is useful in understanding some of the processes that are going on.

We are going to assume that all the power is from the fission reaction – i.e. we are going to ignore the decay heat contribution to the power.

So for a given power the number of fissions per second necessary is given by

[1]

where

is the number of fission events per second – i.e. dF/dt

is the power

is the average energy per fission

Not all of the energy released in the fission event (about 200 MeV – see ‘Whats a Watt’ if you do not know what this means) stays within the reactor – some energy is lost by radiation leaving the reactor vessel. This includes neutrons and neutrinos. So the net power is more like 190 MeV.

We can now estimate how many fission events we need to generate 1MW of power.

1eV = 1.6×10^{-19} J

1MeV = 1.6×10^{-13} J

so 190MeV/fission is 190 x 1.6×10^{-13} = 3.04×10^{-11} J/fission

1MW = 1×10^{6} J/s

Therefore using equation [1] we find that we need 1×10^{6}/3.04×10^{-11} = 3.29×10^{16} fissions per second to generate 1MW. To generate 1GW we will need 1000 times this which is 3.29×10^{19} fissions per second.

If we want to calculate the total number of fissions (*F*) we simply have to multiply by the time T. Note that power (*P*) times time (*T*) is energy.

[2]

We now want to look at how many fission events happen for every tonne of uranium in the reactor. This depends on the ‘burnup’ of the fuel which is measured in Gigawatt days per tonne of Uranium (GWdays/TU).

There are 24x60x60 = 86400 seconds in a day. So if we have a burnup of 50GWdays/TU this is 50×86400 = 4.32×10^{6} Gigawatt seconds per TU – i.e. 4.32×10^{6} Gigajoules. This will require 4.32×10^{6} x 3.29×10^{19} = 1.42×10^{26} fissions.

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