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

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}.)