A thermometer with first-order time constant = 0.1 min and gain = 1.0 is placed in a temperature bath (25^∘C). After the thermometer comes to equilibrium with the bath, the temperature of the bath is increased linearly at a rate of 1^∘ /min. 

(a) What is the difference between the measured temperature Tm and the bath temperature T at t = 0.1 min and t = 1.0 min after the change in temperature?
(b) What is the maximum deviation between T_m (t) and T (t)? When does it occur? 

(c) Plot both T(t) and T_m(t) to 3 mins. For large values of t, determine the time lag between T_m and T.