A mercury thermometer shows the temperature of an environment as 20C. Then, this thermometer is immersed in boiling water. After 6 seconds, the thermometer shows 82C and 6 seconds after that, it shows 96C. Finally, the temperature seen after almost 1 minute is 100C. After that, the thermometer is taken out of the boiling water and placed in its place in the environment. The temperature it shows after 6 seconds is 83C and the temperature it shows after 6 seconds is 69C.

(a) Does this thermometer show first order behavior in boiling water? If yes, calculate the time constant of the thermometer. (b) Does this thermometer show first order behavior during cooling in the environment? If yes, calculate the time constant during cooling. (c) Explain the reason why the time constants of the same thermometer during heating and cooling have different values.