Question

Relation between alpha beta and gamma in thermal expansion derivation

Answer 1

⚡⚡HERE IS YOUR ANSWER

gamma is equal to thrice alpha

Answer 2

This is regarding linear , areal, volume expansion of substances.

ΔL = α L ΔT

Area of a square sheet of dimensions L * L:

 = A+ΔA = (L+ α L ΔT)² = L² + 2 α L² ΔT   ignoring α² terms (too small).

ΔA = 2 α A ΔT

β = ΔA/A  = 2 α

Volume = V = L³

Changed volume = V+ ΔV = (L + α L ΔT)³

        = L³ + 3 α L³ ΔT  +  terms with α² or α³  ignored (too small)

ΔV = 3 α V ΔT

=>  gamma = ΔV/V = 3 α