A thermometer having first order dynamics is placed in a temperature bath of 30C and after reaching the thermometer at steady state, the temperature of the bath is varied in sinusoidal manners about its average temperature of 30C with amplitude of 10C. If the period of oscillation is 0.4min/cycle and the time constant of the thermometer is 6 sec, determine the following: (i) Amplitude ratio (ii) Phase lag (iii) lag (iv) Maximum and minimum temperature of the thermometer