11.2 These devices are usually first order, and we can use Eq. 11.9a (response of a first order system to a step input) for this purpose:

           

                

t(sec)

0.1

1

10

t98%(sec)

0.391

3.91

39.1

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11.4

For a thermocouple (first order system) to closely follow the temperature variation, time constant of the thermocouple (t) should be much smaller than the time scale (period) of temperature variation, tthermo<<tvariation.  All thermocouples of problem 11.2 satisfy this condition.

Note: the smaller the thermocouple, the more closely it will follow the temperature variation of the building.