Two rods are connected as shown. The rods are of same length and same cross sectional area. In steady state, the temperature `(theta)` of the interface will be -

Options

A. `60^(@)C`
B. `73.3^(@)C`
C. `46.7^(@)C`
D. `37.3^(@)C`

Explanation

using function rule at function point
`I_(1)+I_(2)=0`
`(T-20)/(R_(1))+(T-100)/(R_(2))=0`
where `R_(1)=(l)/(KA)` `R_(2)=(l2KA)`
`(T-20)/(l//KA)+(T-100)/(l//2kA)=0`
`T-20+2T-200=0`
on solving `T=(220)/(3)=73.33^(@)C`