# Temperature coefficient

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:

${displaystyle {frac {dR}{R}}=alpha ,dT}$

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

${displaystyle alpha Delta Tll 1}$

, 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:

${displaystyle R(T)=R(T_{0})(1+alpha Delta T),}$

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.

## . . . Temperature coefficient . . .

 This section may be confusing or unclear to readers. In particular, it’s unclear whether this refers to a general negative temperature coefficient or concerning electrical conductivity specifically. (January 2016)

Most ceramics exhibit negative temperature dependence of resistance behaviour. This effect is governed by an Arrhenius equation over a wide range of temperatures:

${displaystyle R=Ae^{frac {B}{T}}}$

where R is resistance, A and B are constants, and T is absolute temperature (K).

The constant B is related to the energies required to form and move the charge carriers responsible for electrical conduction  hence, as the value of B increases, the material becomes insulating. Practical and commercial NTC resistors aim to combine modest resistance with a value of B that provides good sensitivity to temperature. Such is the importance of the B constant value, that it is possible to characterize NTC thermistors using the B parameter equation:

${displaystyle R=r^{infty }e^{frac {B}{T}}=R_{0}e^{-{frac {B}{T_{0}}}}e^{frac {B}{T}}}$

where

${displaystyle R_{0}}$

is resistance at temperature

${displaystyle T_{0}}$

.

Therefore, many materials that produce acceptable values of

${displaystyle R_{0}}$

include materials that have been alloyed or possess variable negative temperature coefficient (NTC), which occurs when a physical property (such as thermal conductivity or electrical resistivity) of a material lowers with increasing temperature, typically in a defined temperature range. For most materials, electrical resistivity will decrease with increasing temperature.

Materials with a negative temperature coefficient have been used in floor heating since 1971. The negative temperature coefficient avoids excessive local heating beneath carpets, bean bag chairs, mattresses, etc., which can damage wooden floors, and may infrequently cause fires.