A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior of the sensor can be described by a first-order transfer function with a time constant of r in seconds. Consider C and Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before the change) concentration of contaminant and therefore the sensor reading is CAo Ppm (i.e., the values at t= 0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, where t is expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step change). In the previous question, What is the analytical solution of the sensor response with respect to time if: 1. the input, C(t)=5+0.5t 2. sensor time constant is 10 seconds 3. the steady state concentration before change is 5ppm O Cm(t) = 5e O Cm(t) : = -5 + 0. 5t + 5e T0 O Cm(t) = 0. 5t + Sei Cm(t) = 3 +2e TO Cm(t) = -5 + 10e To
A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior of the sensor can be described by a first-order transfer function with a time constant of r in seconds. Consider C and Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before the change) concentration of contaminant and therefore the sensor reading is CAo Ppm (i.e., the values at t= 0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, where t is expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step change). In the previous question, What is the analytical solution of the sensor response with respect to time if: 1. the input, C(t)=5+0.5t 2. sensor time constant is 10 seconds 3. the steady state concentration before change is 5ppm O Cm(t) = 5e O Cm(t) : = -5 + 0. 5t + 5e T0 O Cm(t) = 0. 5t + Sei Cm(t) = 3 +2e TO Cm(t) = -5 + 10e To
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
Related questions
Question
3
Transcribed Image Text:A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior
of the sensor can be described by a first-order transfer function with a time constant of r in seconds. Consider C and
Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before
the change) concentration of contaminant and therefore the sensor reading is CAo ppm (i.e., the values at t = 0). An
alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant
concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, wheret is
expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step
change).
In the previous question, What is the analytical solution of the sensor response with
respect to time if:
1. the input, C(t)=5+0.5t
2. sensor time constant is 10 seconds
3. the steady state concentration before change is 5ppm
Cm(t) =
Ст
SeTo
Cm
m(t) = –5+0. 5t + 5e To
O Cm(t) = 0.51 + Sei
O
Cm(t) = 3 + 2e T0
OCm(t) = -5 + 10e
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The