You are hired to build a laser transmissometer to monitor particulate concentrat

Question

You are hired to build a laser transmissometer to monitor particulate concentration in a smoke stack with

an accuracy of at least (+-)5%. The instrument works by shining a laser beam through the exhaust gases and measuring the transmitted beam intensity on a transducer. Laser beam absorption is described by:

where T is the transmittance, Io the intensity of the laser beam at the laser head, I the transmitted intensity,

C the particulate concentration, E the extinction coecient, L the diameter of the smoke stack.

Assume the uncertainty on T ,E ,L is (+-)0.5%.

(a) Plot wc/C vs T. Is this technique acceptable to measure the concentration with the required precision?

(b) How could you decrease the transmittance to increase your accuracy?

You are hired to build a laser transmissometer to monitor particulate concentration in a smoke stack with an accuracy of at least (+-)5%. The instrument works by shining a laser beam through the exhaust gases and measuring the transmitted beam intensity on a transducer. Laser beam absorption is described by: T = I/Io = exp(-C middot E middot L) where T is the transmittance, Io the intensity of the laser beam at the laser head, I the transmitted intensity, C the particulate concentration, E the extinction coecient, L the diameter of the smoke stack. Assume the uncertainty on T ,E ,L is (+-)0.5%. Plot wc/C vs T. Is this technique acceptable to measure the concentration with the required precision? How could you decrease the transmittance to increase your accuracy?

Explanation / Answer

we have

T= e^-(CEL)

so lnT= -(CEL)

ln(-lnT))= lnC+ lnE+ lnL

dc/C = -1/TlnT

so draw the curve like this

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