Question

What is the relationship between area expansivity and volume expansivity

Answer 1

change in length / Length = coef of expansion * change in temp.
Linear:
If you have a cube and heat it , how much does the length change?
change in length = delta L= Length * coef of expansion * change in temp
AREA
Surface Area, two dimensions, side length L:
Old area = 6 L^2
New area = 6(L + delta L)^2 = 6 (L+2 L delta L + delta L ^2)
change in area = 12 L delta L + 6 delta L^2
if delta L^2 << delta L
change in area = 12 L delta L = 12 L* Length * coef of expansion * change in temp
= 12 L^2 * coef of expansion * change in temp
VOLUME:* coef of expansion * change in temp
Old volume = L^3
New volume = (L+ delta L)^3 = L^3+3L^2deltaL+3LdeltaL^2 + deltaL^3
change in volume = 3 L^2 delta L
= 3 L^2 * L * coef of expansion * change in temp
= 3 L^3 * coef of expansion * change in temp