Temperature affects reactivity in a number of ways. The temperat­ure of the structure affects the dimensions of the reactor core and sometimes the relative position of the various parts: the densities of all the materials depend on temperature (but the most important effects arise from changes in the density of the coolant), and the temperature of the fuel affects the resonance self-shielding in the fuel materials. The various effects are discussed in detail by Hummel and Okrent (1970).

If the temperature changes are small the resulting changes in dimensions, density and self-shielding are also small in most cases and proportional to the temperature changes. First-order perturba­tion theory is valid and the resulting reactivity changes are, approxim­ately at least, linear and independent. As a result it is useful to express temperature-induced reactivity changes as reactivity coefficients of the form dp/dTi, where T is the temperature in question (the coolant inlet temperature, for example, or the mean fuel temperature) and dp/dT can be taken to be constant and independent of all the Ti.

This approximation breaks down in some cases. It may not be true in normal operation if there is intermittent contact between bowing fuel elements, and it is certainly untrue in the extreme conditions that may be encountered in an accident — if the coolant boils, for example, or if the fuel temperature rises very high.