A thermocouple is a temperature-measurement device that consists of two dissimilar metal wires joined at one end. An oversimplified diagram follows. 

A voltage generated at the metal junction is read on a potentiometer or millivoltmeter. When certain metals are used, the voltage varies linearly with the temperature at the junction of the two metals: 

V(mV) = aT(°C) + b 

An iron-constantan thermocouple (constantan is an alloy of copper and nickel) is calibrated by inserting its junction in boiling water and measuring a voltage V = 5.27 mV, and then inserting the junction in silver chloride at its melting point and measuring V = 24.88 mV. 

(a) Derive the linear equation for V(mV)in terms of T(°C). Then convert it to an equation for T in terms of V. 

(b) If the thermocouple is mounted in a chemical reactor and the voltage is observed to go from 10.0 mV to 13.6 mV in 20 s, what is the average value of the rate of change of temperature, dT/dt, during the measurement period? 

(c) State the principal benefits and disadvantages of thermocouples.

Transcribed Image Text:

Metal 1 POTENTIOMETER V(mV) Metal 2