A thermocouple has the following characteristics when it is immersed in a stirred bath: Mass of thermocouple = 1 g Heat capacity of thermocouple = 0.25 cal!g oc Heat transfer coefficient = 20 cal!cm2h oc (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 Ts 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 oc reading by a very fast meter. (b) If the thermocouple is initially out of the bath and at room temperature (23 oq, what is the maximum temperature that it will register if it is suddenly plunged into the bath (80 oq and held there for 20 s?

Problem 5.5A thermocouple has the following characteristics when it is immersed in a stirred bath: Mass of thermocouple = 1 g Heat capacity of thermocouple = 0.25 cal/g °C Heat transfer coefficient = 20 cal/cm h °C (for thermocouple and bath) Surface area of thermocouple = 3 cm 2(a) Derive a transfer function model for the thermocouple relating the change in its indicatedoutput T to the change in the temperature of its surroundings Ts assuming uniform temperature(no gradients in the thermocouple bead), no conduction in the leads, constant physicalproperties, and conversion of the millivolt-level output directly to a oc reading by a very fastmeter.(b) If the thermocouple is initially out of the bath and at room temperature (23 °C), what is themaximum temperature that it will register if it is suddenly plunged into the bath (80 °C) and heldthere for 20 s Step-by-step solution Step 1 of 7 ^(a)Consider the energy balance for the thermocouple. dT mC dt = hA(T sT)Here,m is mass of thermocouple,C is the heat capacity of thermocouple ,h is the heat transfer coefficient,A is surface area of thermocouple, andt is the time is sec.