Editing Temperature coefficient (section)

==Temperature coefficient of reactivity==
In [[nuclear engineering]], the temperature coefficient of reactivity is a measure of the change in reactivity (resulting in a change in power), brought about by a change in temperature of the reactor components or the reactor coolant.  This may be defined as

:<math>\alpha_{T} = \frac{\partial \rho}{\partial T}</math>

Where <math>\rho</math> is [[Nuclear chain reaction#Effective neutron multiplication factor|reactivity]] and ''T'' is temperature.  The relationship shows that <math>\alpha_{T}</math> is the value of the [[partial differential]] of reactivity with respect to temperature and is referred to as the "temperature coefficient of reactivity". As a result, the temperature feedback provided by <math>\alpha_{T}</math> has an intuitive application to [[passive nuclear safety]]. A negative <math>\alpha_{T}</math> is broadly cited as important for reactor safety, but wide temperature variations across real reactors (as opposed to a theoretical homogeneous reactor) limit the usability of a single metric as a marker of reactor safety.<ref>Duderstadt & Hamilton 1976, pp. 259–261</ref>

In water moderated nuclear reactors, the bulk of reactivity changes with respect to temperature are brought about by changes in the temperature of the water. However each element of the core has a specific temperature coefficient of reactivity (e.g. the fuel or cladding). The mechanisms which drive fuel temperature coefficients of reactivity are different from water temperature coefficients. While water expands [[Water (properties)#Density of water and ice|as temperature increases]], causing longer neutron travel times during [[Neutron moderator|moderation]], fuel material will not expand appreciably. Changes in reactivity in fuel due to temperature stem from a phenomenon known as [[doppler broadening]], where resonance absorption of fast neutrons in fuel filler material prevents those neutrons from thermalizing (slowing down).<ref>Duderstadt & Hamilton 1976, pp. 556–559</ref> {{Further|Fuel temperature coefficient of reactivity}}