Two bars of equal length and the same cross-sectional area but of different thermal conductivities,` k_(1)` and `k_(2)`, are joined end to end as shown in figure-4.36. One end of the composite bar is maintained at temperature `T_(h)` whereas the opposite end is held at `T_(c)`.
If there are no heat losses from the sides of the bars, the temperature `T_(j)` of the junction is given by :

Options

A. `(k_(2))/(k_(1))((T_(h)+T_(c)))/(2)`
B. `(k_(2))/(k_(1)+k_(2))(T_(h)+T_(c))`
C. `(k_(1)+k_(2))/(k_(2))((T_(h)+T_(c)))/(2)`
D. `(1)/(k_(1)+k_(2))(k_(1)T_(h)+k_(2)T_(c))`

Answer

D

Explanation

We use
`(k_(1)A(T_(h)-T_(j)))/(l) =(k_(2)A(T_(j)-T_(e)))/(l)`
`k_(1)T_(h)-T_(1)k_(l)=k_(2)T_(j)-k_(2)T_(c)`
`T_(j)(k_(1)+k_(2))=k_(1)T_(h) + k_(2)T_(c)`
`T_(j) =(k_(1)T_(h)+k_(2)T_(c))/(k_(1)+k_(2))`