Answer
(a) The heat flow rate through both rods must be the same.
(b) $89cm$
Work Step by Step
(a) We know that the heat will from one rod to the other. Thus, the heat flow rate through both rods must be the same.
(b) We can find the length of the aluminum rod as follows:
$L_{Al}=(\frac{K_{Al}}{K_{Pb}})(\frac{\Delta T_{Al}}{\Delta T_{Pb}})L_{Pb}$
We plug in the known values to obtain:
$L_{Al}=(\frac{217}{34.3})(\frac{80-50}{50-20})(14)$
$L_{Al}=89cm$
