need step by step and proper hand written solution sir/ma'am

area of temperatured D A Thermocouple has the following charactertste when it is immersed is stirred bath: mass of thermocouple = 19; Heat capacity of : thorno couple = 0.25 Callgic; Heat transter coefficient = 20 cal/cm2 6C C for thermocouple a c and bath) Surface thermocouple = 3cm? a) Derive a transfer function model for the thermocouple recating the change in its indicated output 7 to the changes its surrounding Ts anuming uniform temperature Cno gradient in therno couple bead), no conduction in the leads, constant physical properties conversion of the millivolt-level output directly to ac reading by b) If the thermocouple is initially out of the bath and at room temperature (23c), what is the maximum temperature that it will register if it is Suddenly plunged into the bath (80C) and hold there for 20 s? Plot the response of the thermocouple. the and a very fast meter. X X Need Step by step, pooper hand written solution. (Step by step solution ) needed