11.10 Thermocouple is a first order system. As derived in Ex. 11.1, the response of the thermocouple is represented by:
Þ
or
By drawing vs. t, the slope of the line be the negative inverse of the time constant, t. In this case:
DT_{i} = T_{final}T_{i} = 020 = 20 °C
DT = T_{final}T = 0T = 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.