A , B and C are the three identical conductors but made from different materials . They are kept in contact as shown . Their thermal conductivities are K , 2K and `(K)/(2)` . The free end of A is at `100^(@) C` and the free end of C is at `0^(@)C` . During steady state , the temperature of the junction of A and B is nearly .... `""^(@) C` .

Options

A. `37^(@)C`
B. `71^(@)C`
C. `29^(@)C`
D. `63^(@)C`.

Answer

B

Explanation

Let R be the thermal conductivity of conductor, then thermal conductivity of conductor `B=(R )/(2)` and thermal conductivity of conductor `C=2R`.

`:.` Heat current, `H=(100^(@)-0^(@))/(R+(R)/(2)+2R)=(200)/(7R)`
If T. be the temperature of the junction of A and B, then
`H=(100-T.)/(R)` or `(200)/(7R)=(100-T.)/(R)`
or `T.=(500)/(7)=71^(@)C`.
So, correct choice is (b).