The measuring junction of a type-K thermocouple is quickly transferred from warm

Question

The measuring junction of a type-K thermocouple is quickly transferred from warm water to an ice-water bath. The reference junction is always maintained at 0 degree C. At lime t = 0 s the measured voltage output from the circuit is 3.99 mV. The effective time constant of the thermocouple in the ice-water bath is known to be 0.05 seconds. Determine the following; the initial measuring junction temperature (degree C) the voltage output (mV) at 0.05 seconds the apparent measuring junction temperature (to the nearest degree C) at 0.12 seconds

Explanation / Answer

i) From the standard table of Thermocouple of type K,

we get T=97.43 C for 3.99 mV, which is initial measuring junction temperature.

ii) In one time-step response of the system decays to (1/e)th value of its initial value. So V=3.99/e=1.47 mV

iii) We have V=Vo*exp(-t/tau)

=3.99*exp(0.12/0.05)

=0.362 mV

From the standard table, for this voltage we get, T=9.13 C

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