11.10 Thermocouple is a first order system. As derived in Ex. 11.1, the response of the thermocouple is represented by:

or

By drawing  vs. t, the slope of the line be the negative inverse of the time constant, t.  In this case:

DTi = Tfinal-Ti = 0-20 = -20 C

DT = Tfinal-T = 0-T = -T C

t

T(c)

ln

0.1

16.7

0.835

-0.180

0.5

8.1

0.405

-0.903

1

3.3

0.165

-1.802

2

0.6

0.03

-3.507

3

0.1

0.005

-5.298

 

 

A quick method to find the slope is to pick two points. Selecting t = 0.1 and t = 1 sec, we have:

 then

 

Alternatively, we could use linear regression on the data for  vs. t. The resulting time constant is 0.569 sec., 3% higher than the above value.