Home
Class 11
PHYSICS
A thick spherical shell of inner and out...

A thick spherical shell of inner and outer radii r and R respectively has thermal conductivity `k = (rho)/(x^(n))` , where `rho` is a constant and x is distance from the centre of the shell. The inner and outer walls are maintained at temperature `T_(1)` and `T_(2) (lt T_(1))`
(a) Find the value of number n (call it `n_(0)`) for which the temperature gradient remains constant throughout the thickness of the shell.
(b) For `n=n_(0)`, find the value of x at which the temperature is `(T_(1)+T_(2))/(2)`
(c) For `n = n_(0)`, calculate the rate of flow of heat through the shell.

Promotional Banner

Similar Questions

Explore conceptually related problems

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 spherical shell of inner radius R_(1) and outer radius R_(2) is having variable Where 'r' is the distance from the centre Two surface of the shell are maintained at temperature T_(1) respectively (T_(1) ltT_(2)) The heat current flowing through the shell would be .

A hollow tube has a length l, inner radius R_(1) and outer radius R_(2) . The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature T_(1) and T_(2) (T_(2)gtT_(1) (b) the inside of the tube is maintained at temperature T_(1) and the outside is maintained at T_(2) .

A hollow tube has a length l, inner radius R_(1) and outer radius R_(2) . The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature T_(1) and T_(2) (T_(2)gtT_(1)) (b) the inside of the tube is maintained at temperature T_(1) and the outside is maintained at T_(2) .

A hollow tube has a length l, inner radius R_(1) and outer radius R_(2) . The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature T_(1) and T_(2) (T_(2)gtT_(1)) (b) the inside of the tube is maintained at temperature T_(1) and the outside is maintained at T_(2) .

A spherical conducting shell of inner radius r_1 and outer radius r_2 has a charge Q. A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

A spherical conducting shell of inner radius r_1 and outer radius r_2 has a charge Q. A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell ?

A spherical conducting sheel of inner redius s_1 and outer radius r_2 has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell ?