# Temperature coefficient

the temperature coefficient is the relative change physical dimension during a change of temperature of 1K (Kelvin).

Generally math

< X> (T) applies = X (T_0) \ cdot (1 + \ alpha \, (T-T_0) + \ beta \, (T-T_0) ^2 + \ gamma \, (T-T_0) ^3 +… )< /math>
• X = physical dimension
• T = temperature
• T 0 = Bezugstemperatur, usually 20 °C
• α = temperature coefficient 1. Order in the temperature range Δ T = TT 0, angebenen in [K −1]
• β = temperature coefficient 2. Order in the temperature range, angebenen in [K −2]
• γ = temperature coefficient 3. Order in the temperature range, it angebenen into [K −3]

it is to be seen that the temperature dependence is generally nonlinear. This is to be particularly considered with the development from sensitive sensors to. Since however usually linear characteristic are wished, one uses bridging and difference circuits around at least the coefficients with the largest not linear influence on the characteristic (the 2. To suppress order).

For most applications the Temperaturkoeffizenten of higher orders can be neglected however. One uses then a simple linearization of the knowing LINE:

[itex] X (T) = X (T_0) \ cdot (1 + \ alpha \, (T-T_0))[/itex]

Temperature coefficients gives it for the length and the volume (see thermal expansion), the pressure, the electrical resistance and other sizes. A simple linear connection is present generally only in a limited temperature range. Exception: for ideal gases the temperature coefficients for pressure change and variation in volume = 1/273 are K -1.

## temperature coefficient of the electrical resistance

the temperature dependence of the electrical resistance and thus the elements (lines, resistances) must be always taken into account during the construction by building groups and the interpretation by circuits. On the other hand this characteristic is also used, z. B. with resistance thermometers.

Since the temperature coefficient of the electrical resistance is not linear, there is Pt100 of polynomials for example for the standardized resistance thermometer for the computation of the absolute temperature from the measured resistance.

### practical noticing set

the temperature coefficient α indicates, around how much Ω each ohm per 1 Kelvin changes.

With the leader materials important in electro-technology copper and aluminum can be counted in the temperature range 0 to 50°C for estimations on the value 0.4% K -1.

Resistance temperature coefficients of some materials metals pure with
20 °C α K -1 alloys α K of -1 nonmetals α K -1
aluminum (99.5%) 4.0 * 10 -3 Aldrey (AlMgSi) 3.6 * 10 -3 carbon
lead 4.22 * 10 -3 feather/spring bronze (SnBz 4 Pb) 0.5 * 10 -3 arc carbon 0.5 * 10 -3
iron (pure) 6.57 * 10 -3 Konstantan (CuNi 44) ±0,04 * 10 -3
gold 3.98 * 10 -3 Manganin (CuMn 12 never) 0.01 * 10 -3
copper (99.9%) 3.9 * 10 -3 brass (ms 63) 1.3 * 10 -3
platinum 3.8 * 10 -3 Nickelin (CuNi 30 Mn) 0.15 * 10-3
mercury 0.9 * 10 -3 soft irons (4% SI) 0.9 * 10 -3
silver 4.1 * 10 -3