The time constant of a thermocouple is
A. The time taken to attain 100% of initial temperature difference
B. The time taken to attain 63.2% of initial temperature difference
C. The time taken to attain 50% of initial temperature difference
D. The minimum time taken to record a temperature reading
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
The thermal time constant indicates a time required for a thermistor to respond to a change in its ambient temperature.
When the ambient temperature is changed from T1 to T2, the relationship between the time elapsed during the temperature change t (sec.) and the thermistor temperature T can be expressed by the following equation.
\(T = \left( {{T_2} - {T_1}} \right)\left( {1 - \exp \left( {\frac{t}{τ }} \right) + {T_1}} \right)\)
τ (tau in sec.) in the equation denotes the thermal time constant.
Now, assuming t and τ (tau) are equal (t = τ), the equation can be expressed as follows.
T = (T2 – T1) (1-e-1) + T1
\(\frac{{T - {T_1}}}{{{T_2} - {T_1}}} = 1 - {e^{ - 1}} = 1 - \frac{1}{{2.718}} = 0.632\)
This shows that the constant τ (sec.) is defined as a time for the thermistor to reach 63.2% of the total difference between its initial and final body temperatures.
Note:
The temperature change rate at n times the constant τ (sec.) is as follows, showing that the thermistor body temperature reaches its ambient temperature approximately within 7 times the constant.
τ = 63.2%, 2τ = 86.5%, 3τ = 95.0%, ・・・・ 7τ ≒ 100%
