In the figure ABC is a conducting rod whose lateral surfaces are insulated. The length of the section AB is one-half of that of BC, and the respective thermal conductivities of the two sections are as given in the figure. If the ends A and C are maintained at `0^(@)C` and `70^(@)C` respectively, the temperature of junction B in the steady state is

Options

A. `30^(@)C`
B. `40^(@)C`
C. `50^(@)C`
D. `60^(@)C`

Answer

A

Explanation

Heat current in both the rods are equal
or `H_(CB) = H_(BA)`
or `(theta_(C)-theta_(B))/(2l//3KA)=(theta_(B)-theta_(A))/(l//2KA)`
`therefore` `3/2(70-theta_(B))= 2(theta_(B)-0)`
or `theta_(B) = 30^(@)C`