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An infinite series of same-volume CSTR units can model the behavior of a PFR having the same total volume. Show that for a reaction that has a first-order reaction rate, the residence time, Ti, in a single CSTR in the series can be written as T₁ = (1/k) [(CA/CAN) (+) – 1] where N is the number of CSTR units, CAO and CAN are the concentrations of component A entering unit 1, and leaving unit N respectively, and k is the specific rate of reaction (or the rate constant). Also, show that as N approaches infinity, TN = (1/k) In (CA0/CAN), which is the same as the residence time for a PFR having the same total volume as the CSTRS in series.

An infinite series of same-volume CSTR units can model the behavior of a PFR having the same total volume. Show that for a reaction that has a first-order reaction rate, the residence time, Ti, in a single CSTR in the series can be written as T₁ = (1/k) [(CA/CAN) (+) – 1] where N is the number of CSTR units, CAO and CAN are the concentrations of component A entering unit 1, and leaving unit N respectively, and k is the specific rate of reaction (or the rate constant). Also, show that as N approaches infinity, TN = (1/k) In (CA0/CAN), which is the same as the residence time for a PFR having the same total volume as the CSTRS in series.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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An infinite series of same-volume CSTR units can model the behavior of a PFR having the same total volume. Show that for a reaction that has a first-order reaction rate, the residence time, T₁, in a single CSTR in the series can be written as T₁ = = (1/k) [(CA0/CAN) ) ( 7 ) 1] where N is the number of CSTR units, CAO and CAN are the concentrations of component A entering unit 1, and leaving unit N respectively, and k is the specific rate of reaction (or the rate constant). Also, show that as N approaches infinity, TN = (1/k) ln(CA0/CAN), which is the same as the residence time for a PFR having the same total volume as the CSTRs in series.
Transcribed Image Text:An infinite series of same-volume CSTR units can model the behavior of a PFR having the same total volume. Show that for a reaction that has a first-order reaction rate, the residence time, T₁, in a single CSTR in the series can be written as T₁ = = (1/k) [(CA0/CAN) ) ( 7 ) 1] where N is the number of CSTR units, CAO and CAN are the concentrations of component A entering unit 1, and leaving unit N respectively, and k is the specific rate of reaction (or the rate constant). Also, show that as N approaches infinity, TN = (1/k) ln(CA0/CAN), which is the same as the residence time for a PFR having the same total volume as the CSTRs in series.
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