Question 4 Two thermocouples are placed in an air stream whose temperature is varying sinusoidally. The temperature responses of each thermocouple are recorded for a range of frequencies, with the phase

angle between the two measurements tabulated below. The standard thermocouple is known to have first-order dynamics with a time constant of 0.15 minutes when operating in air. Show the unknown thermocouple also displays first order behavior and determine its time constant. After approximately 30 seconds the standard themocouple shows a sinusoidal variation in air temperature between 96 and 104 degrees Celcius, at a rate of two cycles per minute. What error will the standard thermocouple report in this instance if left to measure the air temperature indefinitely? CHEM ENG 4050: Advanced Chemical Engineering Advanced Control Table 1. Thermocouple phase difference for Question 4. Frequency (cycles/min) 0.05 0.1 0.2 0.4 0.8 1.0 2.0 4.0 Phase Difference (deg) 4.5 8.7 16.0 24.5 26.5 25.0 16.7 9.2