Solution
= Solution
At late times $C\to1/2$ and thermal equilibration requires $b_0C-b_1T=0$. Hence $\boxed{T(\infty)=b_0/(2b_1)}$. Both $t\gg k^{-1}$ and $t\gg b_1^{-1}$ ensure that the exchange and thermal transients have decayed.
= Solution
At late times $C\to1/2$ and thermal equilibration requires $b_0C-b_1T=0$. Hence $\boxed{T(\infty)=b_0/(2b_1)}$. Both $t\gg k^{-1}$ and $t\gg b_1^{-1}$ ensure that the exchange and thermal transients have decayed.