a$.$ Explain how a batch reactor is related to a plug flow reactor.

b$.$ Explain the units of flux $($remember it is a vector$).$

c$.$ Consider a system involving transport and transformation processes. How can a comparison between the characteristic residence time for the chemical reaction $(\backslash$tau r$)$ and the hydraulic residence time $(\backslash$Theta $)$ be used to simplify analysis? Consider both limits $\backslash$tau r $<<\backslash$Theta and $\backslash$tau r $>>\backslash$Theta as well as the case of $\backslash$tau r ~$\backslash$Theta

d$.$ Explain conceptually why a PFR is more efficient than a CMFR$$given the same residence time and rate constant$$for a first$-$order decay reaction at steady state.