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 10 s, c:n(s) C'(s) 1 lOs + 1 where C' is the actual contaminant concentration and C'm is the measured value. Both are expressed as deviation variables (e.g., C' = C- C). The nominal concentration is C = 5 ppm. Both C and Cm have values of 5 ppm initially (i.e., the values at t = 0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the contaminant concentration C gradually increases according to the expression C(t) = 5 + 0.2t, where tis expressed in seconds. After the actual contaminant concentration exceeds the environmental limit, what is the time interval, !1t, until the alarm sounds?

Problem 5.3A 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 witha time constant of 10 s, C m) = 1 C s) 10s + 1where C' is the actual contaminant concentration and C' is mhe measured value. Both areexpressed as deviation variables (e.g., C = C C . The nominal concentration is C = 5ppm. Both C and C m have values of 5 ppm initially (i.e., the values at t = 0). An alarmsounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that thecontaminant concentration C gradually increases according to the expression C(t) = 5 +0.2t, where t is expressed in seconds. After the actual contaminant concentration exceedsthe environmental limit, what is the time interval, t, until the alarm sounds Step-by-step solution Step 1 of 6 ^Consider that the dynamic behavior of the sensor is a given first-order transfer function witha time constant of 10s. C m) 1 C s) = 10s + 1 Cm(s) = C(s) ( 1 ) ……….(1) 10s + 1Here Cm is measured value, C is the actual contamination concentration.