A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas streaim. The convective heat transfer co-efficient on the bead surface is 400 W/m$$^2$$K. Thermo-physical properties of thermocouple material are k = 20 W/mK , C = 400 J/kg K and r = 8500 kg/m$$^3$$ . If the thermocouple initially at $$30^\circ$$ C is placed in a hot stream of $$300^\circ$$ C, the time taken by the bead to reach $$298^\circ$$ C, is