Two metal rods A and B of equal lengths and equal cross- sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in ratio 2 : 3 , when the free end of A is maintained at `100^(@)C`, free end of B at `0^(@)C`, the temperature of the junction is

Options

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

Answer

B

Explanation

`K_(A) : K_(B) = 2 : 3`
`Q_(A) = Q_(B)`
`(K_(A)A_(A)(T_(A) - T))/(l_(A))=(K_(B)A_(B)(T - T_(B)))/(l_(B))`
`implies (T_(A)-T)/(T- T_(B))=K_(B)/K_(A)` `(because l_(A)=l_(B),A_(A)=A_(B))`
`implies (100-T)/(T-0)=(3)/(2)`
`implies 200 - 2T = 3T`
`implies 5T = 200`
`therefore T = 40^(@)C`