Consider a thermometer at room temperature 20.0 ◦c. we now place it inside a water tank whose temperature is at 30.0 ◦c. after one minute, it shows the temperature at 29.8 ◦c.

(a) assuming the thermometer follows a 1st-order dynamics, what is its time constant?
(b) if we place the same thermometer in another tank whose temperature increases linearly with a uniform rate of 2◦c/min, and we wait long enough, what would be the measurement error (in ◦c) in the thermometer reading?