Respuesta :
Answer:
γ ≈ 2 α
Explanation:
The thermal expansion of solids in one dimension is given by
ΔL = α L ΔT
If we fear a square side L * L we must find the square area to see its expansion
A = L * L
Square the body warms up the area increases a quantity DA and each side increases a quantity DL
A + DA = (L + ΔL) (L + ΔL)
Let's replace the linear expansion equation
A + Da = (L + α L ΔT) (L + α L ΔT)
A + DA = L² + 2 α L Δt + (α L ΔT)²
A + Da = L2 (1 + 2 α ΔT + α² ΔT²
)
A = L2
ΔA / A + DA / A = (1 + 2 α DT + α² DT²)
1+ DA / A = (1 + 2 α DT + α² ΔT²)
ΔA / A = (2 α ΔT + α² ΔT²)
In general alpha is small (10⁻⁶ C⁻¹ ) and the temperature changes are not very large (100ºC), so we can neglect the quadratic term
ΔA = γ A Δt
γ ≈ 2 α
