The following chart shows the output voltage trending of a t

The following chart shows the output voltage trending of a thermocouple-based temperature measurement device. Initially the temperature was 22.5 degree C. The thermocouple probe was then abruptly inserted into ice water (0.0 degree C). Based on the chart, (1) Determine the sensitivity of the measurement device (note the unit). (2) Estimate the time constant of the device.

Solution

1 the sensitivity of thermocouple is= change in voltage/change in temperature

from graph voltage is changed from 0.9v to 4.1v and temperature is changed from 22.5 degrees to 0 degrees(probe moved to 0)

therefore sensitivity = (0.41-0.9)/(0-22.5) = 21.78mV/degrees Celsius

2 the constant for the system is defined as the time taken reach 36.8 percent value while decreasing

that means T is observed from graph

36.8 percent of voltage of given graph is 0.368(0.9-0.41)+0.41

that is.0.58

the time corresponding to 0.58v is 0.22 sec

so time constant of system is 0.22 sec.