college physic
posted by noah on .
Determine a formula for the change in surface area of a uniform solid sphere of radius r if its coefficient of linear expansion is alpha A (assume constant) and its temperature is changed by Delta T.Assume the temperature chan ge is not large, Delta T^2 ~ 0.

Area A = 4 pi R^2
lnA = ln(4 pi) + 2 ln R
dA/A = 2 dR/R = 2*(alpha)*dT
delta A = 2A*alpha*(delta T)
OR
A at T + deltaT
delta A = 4 pi (R + deltaR)^2  A
= 4 pi R(1 + alpha*deltaT)^2 A
= 4 pi R^2 *[1 + 2*alpha*deltaT +
(alpha*deltaT)^2]  A
= 2*A*alpha*deltaT + A*(alpha*deltaT)^2
(Ignore the second term in deltaT^2) 
TQ^^