A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R that changes when the temperature changes by dT, the temperature coefficient α is defined by the following equation:
d
R
R
=
α
d
T
{\displaystyle {\frac {dR}{R}}=\alpha \,dT}
Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K−1.
If the temperature coefficient itself does not vary too much with temperature and
α
Δ
T
≪
1
{\displaystyle \alpha \Delta T\ll 1}
, a linear approximation will be useful in estimating the value R of a property at a temperature T, given its value R0 at a reference temperature T0:
R
(
T
)
=
R
(
T
0
)
(
1
+
α
Δ
T
)
,
{\displaystyle R(T)=R(T_{0})(1+\alpha \Delta T),}
where ΔT is the difference between T and T0.
For strongly temperature-dependent α, this approximation is only useful for small temperature differences ΔT.
Temperature coefficients are specified for various applications, including electric and magnetic properties of materials as well as reactivity. The temperature coefficient of most of the reactions lies between −2 and 3.