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:
| dR | |
| R |
=\alphadT
If the temperature coefficient itself does not vary too much with temperature and
\alpha\DeltaT\ll1
R(T)=R(T0)(1+\alpha\DeltaT),
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.
Most ceramics exhibit negative temperature dependence of resistance behaviour. This effect is governed by an Arrhenius equation over a wide range of temperatures:
R=
| ||||
| Ae |
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:
R=rinfty
| ||||
| e |
=R0
| ||||
| e |
| ||||
| e |
where
R0
T0
Therefore, many materials that produce acceptable values of
R0
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.
Residual magnetic flux density or B changes with temperature and it is one of the important characteristics of magnet performance. Some applications, such as inertial gyroscopes and traveling-wave tubes (TWTs), need to have constant field over a wide temperature range. The reversible temperature coefficient (RTC) of B is defined as:
RTC=
| |\DeltaBr| | |
| |Br|\DeltaT |
x 100\%
To address these requirements, temperature compensated magnets were developed in the late 1970s.[1] For conventional SmCo magnets, B decreases as temperature increases. Conversely, for GdCo magnets, B increases as temperature increases within certain temperature ranges. By combining samarium and gadolinium in the alloy, the temperature coefficient can be reduced to nearly zero.
The temperature dependence of electrical resistance and thus of electronic devices (wires, resistors) has to be taken into account when constructing devices and circuits. The temperature dependence of conductors is to a great degree linear and can be described by the approximation below.
\operatorname{\rho}(T)=\rho0\left[1+\alpha0\left(T-T0\right)\right]
where
\alpha0=
| 1 | |
| \rho0 |
\left[
| \delta\rho | |
| \deltaT |
| \right] | |
| T=T0 |
\rho0
That of a semiconductor is however exponential:
\operatorname{\rho}(T)=S
| ||||
| \alpha |
where
S
\alpha
B
For both,
\alpha
This property is used in devices such as thermistors.
A positive temperature coefficient (PTC) refers to materials that experience an increase in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid increase with temperature, i.e. a higher coefficient. The higher the coefficient, the greater an increase in electrical resistance for a given temperature increase. A PTC material can be designed to reach a maximum temperature for a given input voltage, since at some point any further increase in temperature would be met with greater electrical resistance. Unlike linear resistance heating or NTC materials, PTC materials are inherently self-limiting. On the other hand, NTC material may also be inherently self-limiting if constant current power source is used.
Some materials even have exponentially increasing temperature coefficient. Example of such a material is PTC rubber.
A negative temperature coefficient (NTC) refers to materials that experience a decrease in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid decrease with temperature, i.e. a lower coefficient. The lower the coefficient, the greater a decrease in electrical resistance for a given temperature increase. NTC materials are used to create inrush current limiters (because they present higher initial resistance until the current limiter reaches quiescent temperature), temperature sensors and thermistors.
An increase in the temperature of a semiconducting material results in an increase in charge-carrier concentration. This results in a higher number of charge carriers available for recombination, increasing the conductivity of the semiconductor. The increasing conductivity causes the resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance.
The elastic modulus of elastic materials varies with temperature, typically decreasing with higher temperature.
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
\alphaT=
| \partial\rho | |
| \partialT |
Where
\rho
\alphaT
\alphaT
\alphaT
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 as temperature increases, causing longer neutron travel times during 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).[5]
In its more general form, the temperature coefficient differential law is:
| dR | |
| dT |
=\alphaR
Where is defined:
R0=R(T0)
And
\alpha
T
Integrating the temperature coefficient differential law:
| R(T) | |
| \int | |
| R0 |
| dR | |
| R |
=
| T | |
| \int | |
| T0 |
\alphadT~ ⇒ ~
| R(T) | |
| ln(R)\vert | |
| R0 |
=\alpha(T-T0)~ ⇒ ~ ln\left(
| R(T) | |
| R0 |
\right)=\alpha(T-T0)~ ⇒ ~ R(T)=R0
| \alpha(T-T0) | |
| e |
Applying the Taylor series approximation at the first order, in the proximity of
T0
R(T)=R0(1+\alpha(T-T0))
The thermal coefficient of electrical circuit parts is sometimes specified as ppm/°C, or ppm/K. This specifies the fraction (expressed in parts per million) that its electrical characteristics will deviate when taken to a temperature above or below the operating temperature.