(b) A thermometer is regarded as a first-order instrument where a time delay exists in its response to a sudden change a

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B A Thermometer Is Regarded As A First Order Instrument Where A Time Delay Exists In Its Response To A Sudden Change A 1 (82.31 KiB) Viewed 25 times

(b) A thermometer is regarded as a first-order instrument where a time delay exists in its response to a sudden change at its input. The response equation of the thermometer is expressed as, T(t) - To = (Tf - To)(1-e¯½) where T(t) (°C) is the temperature of the thermometer at time t(s); To (°C) and T (°C) are the initial and final temperatures of the process being measured, respectively; and (s) is the time constant. (i) If the thermometer gives a measurement of 44 °C (To) just before a sudden change in the process which is 80 °C (T), and reads 57 °C at time 4.5 s after the change, determine and thus write down the response equation for the thermometer. Show all your working steps. (ii) Determine the temperature reading 6 s after the occurrence of the sudden change specified in (i). [6 marks]