Question

Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductitvity of B is thrice that of C and half that of A. The effective thermal conductivity of rod A)
A. `(1)/(3)K_(A)`
B. `3 K_(A)`
C. `2 K_(A)`
D. `(2)/(3)K_(A)`

Answer 1

Correct Answer - A
Let L be the length and A be the area of cross-section of each rod. Given
`K_(B) =3 K_(C), K_(B) =(1)/(2)K_(A)`
`:. K_(C)=(1)/(3)K_(B) =(1)/(3)xx(1)/(2)K_(A) =(1)/(6)K_(A)`
Thermal resistance of rod A, `R_(A) =(L)/(K_(A)A)`
Thermal resistance of rod B, `R_(B) =(L)/(K_(B)A) =(2L)/(K_(A)A)`
Thermal resistance of rod C, `R_(C) =(L)/(K_(C)A) =(6L)/(K_(A)A)`
Here, the rods connected in series. If K is effective thermal conductivity of the system, and `R_(s)` is the total thermal resistance of the system then `R_(S) =R_(A) + R_(B) + R_(C)`
`:. (3L)/(KA) =(L)/(K_(A)A) + (2L)/(K_(A)A) + (6L)/(K_(A)A) = (9L)/(K_(A)A)`
or `(3)/(K) = (9)/(K_(A))` or `K=(K_(A))/(3)`