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 .

Answer

B

Explanation

Temperature is decresing as we are going out Let a distance x from the centre the temperature
gradient is `- (dT)/(dx)` At this location `K = a_(0) Tr`
From `H = -KA ((dT)/(dx))` We have
`H = - a_(0) T r xx 4 lambda^(2) xx (dT)/(dr)`
`rArrint_(R_(1))^(R_(2))(Hdx)/(x^(3)) = - int_(T_(1))^(T_(2))4pi_(a)TdT`
`rArr H = (4pia_(0)R_(1)^(2)R_(2)^(2)(T_(1)^(2)-T_(2)^(2)))/(R_(2)^(2)-R_(1)^(2))` .