A thermocouple junction in the form of 4 mm radius sphere is to be used to measure the temperature of a gas stream. The junction is initially at 35 degree Celsius and is placed in a gas stream which is at 300 degree Celsius. The thermocouple is removed from the hot gas stream after 10 seconds and kept in still air at 25 degree Celsius with convective coefficient 10 W/m² K. Find out the time constant of the thermocouple. Assume the thermos-physical properties as given below:
h = 37.5 W/m² K
p = 7500 kg/m³
c = 400 J/kg K