A blacksmith heated a metal whose cubic expansivity is 6.3^-6k-1. The area expansivity of the metal is …….

Answer 1

if s is side of cube
and ds/s /dT = c (coef of linear exp)
ds /s= c dT
original area= s^2
new area = (s+ds)^2 = s^2 + 2 s ds + ds^2
increase in area = 2 s ds+ds^2
for small ds increase = 2 s ds
so increase/s^2 = 2 ds/s = 2 c dT
square coef = 2 *linear coef

Answer 2

original vol =s^3
final vol = (s + ds)^3 = s^3 + 3 s^2 ds + s ds^2 + ds^3
for small ds
change = 3 s^2 ds
change/s^3 = 3 ds /s = 3 c dT
so 3 times the linear and twice the area
so
area coef = 2/3 cubic coef