A thermometer has first-order dynamics with a time constant of 1 sec and is placed in a temperature bath at 120^∘F. After the thermometer reaches steady state, it is suddenly placed in a bath at 140^∘ F for 0 ≤ t ≤ 10 sec. Then it is returned to the bath at 100^∘F.
(a) Sketch the variation of the measured temperature T_m(t) with time.
(b) Calculate T_m (t) at t = 0.5 sec and at t = 15.0 sec. 5.28.