(20pts) A thermocouple junction, which may be approximated as sphere, is to be used for temperature measurement in a gas stream. The convection coefficient between the junction surface and the gas is h = 400 W/m2·K and the junction thermophysical properties are k = 20 W/m·K, c = 400 J/kg·K and rho = 8500 kg/m3. Determine the junction diameter needed for the thermocouple to have a time constant of 2 s. If the junction is at 25 °C and is placed in a gas stream that is at 200 °C, estimate the temperature of the junction after 10 minutes.