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