A rod of uniform cross-section but non-uniform thermal conductivity which vary as `k=k_(0)(x^(2))/(L^(2))(1lexleL)` (as shown in figure) is kept between fixed temperature difference for a long time. Select the correct options(s)

Options

A.
B.
C.
D.

Answer

A, D

Explanation

`I = (k_(0)x^(2))/(L^(2))A(dT)/(dx)rArr underset(T_(H))overset(T)(int)dT=(iL^(2))/(k_(0)A) underset(l)overset(x)(int) (dx)/(x^(2))`
`T-T_(H)=(iL^(2))/(k_(0)A)[(1)/(x)]_(1)^(x)`.