Question

For mixed flow of particles containing a single unchanging size and uniform gas composition, the fraction unconverted for film resistance controlling is ____

(a) \(\int_0^τ\)(-\(\frac{t}{τ}\))\(\frac{e}{t}^\frac{-t}{t}\) dt

(b) \(\int_0^τ\)(1 – \(\frac{t}{τ}\))\(\frac{e}{t}^\frac{-t}{t}\) dt

(c) \(\int_0^τ\)(1 –\(\frac{t}{τ}\))dt

(d) \(\int_0^τ\)(1 – \(\frac{t}{τ}\))\(\frac{e}{t}^\frac{-t}{t}\) dt

I had been asked this question by my college professor while I was bunking the class.

The question is from Design of Fluid Particle Reactors in portion Fluid-Particle Reactions: Kinetics of Chemical Reaction Engineering

Answer 1

Right option is (b) \(\int_0^τ\)(1 – \(\frac{t}{τ}\))\(\frac{e}{t}^\frac{-t}{t}\) dt

For explanation I would say: For a mixed flow reactor, the mean residence time, t in the reactor is, E = \(\frac{e}{t}^\frac{-t}{t}\). For a single size of particles converted in time τ,  1-\(\overline{X_{(B)}}\) = ∫0^τ(1 – XB)\(\frac{e}{t}^\frac{-t}{t}\)dt for an individual particle. For film resistance controlling, XB = \(\frac{t}{τ}.\)