In the previous example, how much additional reactivity has to be added to the core by withdrawing the control rods to keep the core critical when the average fuel temperature rises from 300°C to 1000°C? What is the value of this additional reactivity in pcm and in dollars and cents?
In Example Problem 17.8, the initial reactivity of the core at a temperature of 300°C was ρ = (k−1)/k = 0.0, and the final reactivity of the core (without moving the control rods) would be ρ = (k−1)/k = −0.01/0.99 = −0.0101. Hence, the control rods must add an additional 0.0101 of positive reactivity to the core to keep it critical. This is equivalent to adding 1010 pcm, or since the delayed neutron fraction of U-235 is β = 0.0065, Δρ = 0.0101/β = $1.55.