Consider two rods of equal cross - sectionai area A, one of Aluminium and other of iron joined end to end as shown in figure -4.8. Length of the two rods and their thermal coductivities are `l_(1) , k_(1)`and `l_(2),k_(2)` respectively . If the ends of the rods are maintained at temperature `T_(1)` and `T_(2),(T_(1)gt T_(2))` find the temperature of the junction in steady state .

Explanation

We know in steady state the rate of heat flow or the thermal current throughout the medium remains constant thue have
`((dQ)/(dt))_(At) = ((dQ)/(dt))_(Fe)`
If junction temperature is assumed `T_(x)` then we have

`(k_(1)A(T_(1)-T_(x)))/(l_(1))=(k_(2)A(T_(x)-T_(2)))/(l_(2))`
or`T_(x)=((k_(1)T_(1))/(l_(1))+(k_(2)T_(2))/(l_(2)))/(k_(1)/(l_(1))+(k_(2))/(l_(2)))=(k_(1)l_(2)T_(1)+k_(2)l_(1)T_(2))/(k_(1)l_(2)+k_(2)l_(1))`