Engine Operational
GATE CH 2020 (with Solutions).pdf

Q19

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The square of Thiele modulus, Mₜ, is given byMₜ²=L² k/Deff, where L is the characteristic length of the catalyst pellet, k is the rate constant of a first order reaction, and Dₑ_f_fis the effective diffusivity of the species in the pores. Mₜis a measure of

Options

  1. A.
    rateofreactio2n/rateofexternalmasstransferrateofreactio^2 n / rateofexternalmasstransfer
  2. B.
    rateofporediffusion/rateofreaction
  3. C.
    timescaleofreaction/timescaleofporediffusion
  4. D.
    timescaleofporediffusion/timescaleofreaction

Answer

C

Solution

(M_t)^2 = /frac{L^2k}{D_e_f_f}
(Mt)=/frac/frac/fracK/textDeff.Lrxn/textrate/textDiffusionrate(M_t) = /frac{/frac{/frac{K}{/text{Deff} . L}}{rx^n} /text{rate}}{/text{Diffusionrate}}
=/textength= /text{ength}
characteristicL/intrinsicrxⁿrate/Diffusionrate
..
Thiele modulus = reaction rate / diffusion rate
..
Time scale of the limiting transport mechanism
..
..

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