The Nuclear Reactor — Question 4

Question 4

Constant neutron population requires production to balance all losses

An abstract neutron inventory receives $1.20\times10^{12}$ neutrons/s from fission, with no external source. Absorption removes $9.00\times10^{11}$ neutrons/s and escape removes $3.00\times10^{11}$ neutrons/s. Rates are fixed over a short observation interval.

1. Write the inventory balance, evaluate its initial slope, and explain the meaning of critical balance.

2. If escape increases by 10 percent for 2.00 s while the other stated rates remain fixed, calculate the inventory change.

Question 4 - Solution

Constant neutron population requires production to balance all losses

(a) Method and calculation

$$\frac{dN}{dt}=S-L_a-L_e,\qquad k=\frac{S}{L_a+L_e}=1\quad\text{(critical balance)}.$$$$\boxed{\dot N=1.20\times10^{12}-.90\times10^{12}-.30\times10^{12}=0}.$$

(b) Interpretation and further calculation

$$\boxed{\dot N\prime=-.10(3.00\times10^{11})=-3.00\times10^{10}\,\mathrm{s^{-1}}}.$$$$\boxed{\Delta N=\dot N\prime\Delta t=-6.00\times10^{10}}.$$

Physical check

Zero slope means constant population, not zero neutron motion. This fixed-rate interval is an inventory exercise, not a time-dependent core model.