Question

A metallic sphere having inner and outer radii `a` and `b` respectively has thermal conductivity
`K=(K_(0))/r (alerleb)`
Find the thermal resistance between inner surface and outer surface.
A. `((b-a))/(4piK_(0))`
B. `((b^(2)-a^(2)))/(4piK_(a)ab)`
C. `(4 piK_(0))/((b-a))`
D. none of these

Answer 1

(a) We consider a spherical element of radius `r` and thickness `dr`. The resistance of considered element is
`dR=(dr)/(KA)=(dr)/(K 4pir^(2))=(dr)/((K_(0))/(r^(2))4pir^(2))`
`:. dR=1/(4piK_(0))dr`
The equivalent resistance `R=1/(4piK_(0) int(a)^(b)dr=((b-a))/(4piK_(0))`