A thermocouple has the following characteristics when it is immersed in a stirred bath: Mass of thermocouple – 1g. Heat capacity of thermocouple = 0.25 cal/g °C I-feat transfer coefficient = 20 cat/cm2 h °C (for thermocouple and bath) Surface area of thermocouple = 3 cm2

(a) Derive a transfer function model for the thermocouple relating the change in Its indicated output T to the change in the temperature of Its surroundings T assuming uniform temperature (no gradients in the thermocouple bead), no conduction in the leads, constant physical properties, and conversion of the millivolt-level output directly to a °C reading by a very fast meter.

(b) If the thermocouple is initially out of the bath and at room temperature (23 °C), what is the maximum temperature that it will register if it is suddenly plunged into the bath (80 °C) and held there for 20 s?