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?