Two rods of length `l_(1) and l_(2)` and coefficients of thermal conductivities `k_(1) and K_(2)` are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

Answer

Since they are in series, the rate of flow of heat energy is the same. But the sum of the difference in temperature is the difference across their free ends.
`(##RES_HAT_PHY_XI_C03_E01_006_A01##)`
`:. (theta_(1) -theta) +(theta -theta_(1)) = (theta_(1)- theta_(2))`
i.e `(Q)/(t) (l_(1))/(K_(1)A) +(Q)/(t).(l_(2))/(K_(2)A) = (Q)/(t) ((l_(1)+l_(2)))/(K_(2)A)`
`rArr (l_(1))/(K_(1)) +(l_(2))/(K_(2)) = (l_(1)+l_(2))/(K_(eq)) :. K_(eq) = (l_(1)+l_(2))/((l_(1)/(K_(1))+l_(2)/(K_(2))))`