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 junctions is read on a potentiometer or mill voltmeter. 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-constant an thermocouple (constant an is an alloy of copper and nickel) is calibrated by inserting its junction in boiling water and measuring a voltage V = 5.27mV, and then inserting the junction in silver chloride at its melting point and measuring V = 24.88mV.

(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 10.0mV to 13.6mV in 20s, what is the average value of the rate of change of temperature dT/dt, during the measurement period?