expansionskoefficient

Expansionskoefficient, commonly called expansion coefficient, is a parameter that describes how a quantity changes in response to a change in another variable, typically temperature. The term is used in physics and engineering to characterize the thermal expansion of materials, and in mathematics to refer to the coefficients in a series expansion of a function.

Thermal expansion: For a linear dimension L, ΔL = α L0 ΔT, where α is the linear expansion coefficient (units: 1/K or 1/°C). For area, ΔA ≈ γ A0 ΔT with γ ≈ 2α, and for volume, ΔV ≈ β V0 ΔT with β the volumetric coefficient. In isotropic solids β ≈ 3α. Coefficients depend on temperature and material.

Typical values: metals around 5–30×10^-6 /°C; steel ~11–13×10^-6 /°C; aluminum ~23×10^-6 /°C; copper ~17×10^-6 /°C; glass near 9×10^-6 /°C; plastics can be markedly higher. Coefficients are stored in material datasheets and can vary with temperature.

Measurement and applications: coefficient determined by dilatometry or interferometry; used in design to accommodate expansion in structures, pipes, rails, or electronics to prevent buckling or gaps.

Mathematics: In a function expansion, coefficients quantify contributions of basis functions. For a Taylor series about x0: f(x) = sum a_n (x - x0)^n, where a_n = f^(n)(x0)/n!. In Fourier series: f(x) ~ a0/2 + sum a_n cos(nx) + b_n sin(nx), with coefficients determined by integrals or derivatives.