A thermocouple junction, which may be approximated as a sphere, is to be used for temperature measurement in a gas stream. The convection coefficient between the junction surface and the gas is known to be h = 400 W/m2 ?K, and the junction thermophysical properties are k = 20 W/m?K, Cp = 400 J/kg?K, and ? = 8500 kg/m3 . Determine the junction diameter needed for the thermocouple to have a time constant of 1 s. If the junction is at 25 oC and is placed in a gas stream that is at 200 oC, how long will it take for the junction to reach 199 oC?