Show that the temperature Tx at the interface of a compound slab (see sample problem 23-1) is given by

Consider a long rod of length L and uniform cross section A, in which one end is maintained at the high temperature T_H and the other end at the low temperature T_L. This is a steady state situation: the temperatures and the rate of heat transfer are constant in time. In this situation, every increment of energy that enters the rod at the hot end leaves it at the cold end.
For this case, the equation H = kA ΔT/ Δx will be,
H =kA ΔT/ Δx
= A ΔT/ R
= A (T_H – T_L)/ R (Since, ΔT = T_H – T_L)