Coefficient of expansion

the coefficient of expansion is defined as linear coefficient of expansion or thermal expansion and as volumetric expansion coefficient or cubic coefficient of expansion.

linear Wärmeausdehnungskoeffizient

the linear coefficient of expansion is a measure for the relative length variation, for example a staff of the length <math> L< /math>, per degree of change of temperature. It is a material-specific size of, those for one homogeneous solids defined is through:

<math> \ alpha = \ frac {1} {L} \ cdot \ frac {\ delta L} {\ delta T} </math>

The length variation of a staff when even heating up or cooling around the temperature difference <math> \ delta T< /math> can be computed, by the linear coefficient of expansion <math> \ alpha< /math> the staff material with the staff length <math> L< /math> and the temperature difference <math> \ delta T< /math> one multiplies:

<math> \ Delta L = \ alpha \ cdot L \ cdot \ delta T </math>

volume-specific coefficient of expansion

the volume-specific coefficient of expansion describes the relative change of the volume <math> V< /math> with the temperature <math> T< /math>.

It is defined through:

<math> \ gamma= \ frac {1} {V} \ left (\ frac {\ part V} {\ part T} \ right) _p </math>

To isotropic solids applies <math> \ gamma = 3 \ cdot \ alpha </math>.

The volume-specific coefficient of expansion results, there the mass <math> \ rho (T) \ V (T) cdot </math> , from the density math \ <rho> (T) /math is <temperature independent> as a function of the temperature:

<math> \ gamma= \ frac {1} {\ rho} \ left (\ frac {\ part \ rho} {\ part T} \ right) _p </math>

If the coefficient of expansion is well-known as function of the temperature, then the density results out:

<math> \ rho (T) = \ rho (T_0) \ cdot \ exp \ left (- \ int_ {T_0} ^ {T} \ gamma (T) \ cdot dT \ right) </math>

Here is <math> T_0 </math> any temperature, e.g. <math> T_0 </math> = 298.15 K = 25 °C, with that the density <math> \ rho (T_0) </math> admits is.

Green iron showed that the quotient <math> \ alpha/c_p< /math> between thermal coefficients of expansion <math> \ the alpha< /math> and the specific thermal capacity <math> c_p </math> of the temperature is independent.

see also: Thermal expansion, Wärmeausdehnungskoeffizient