9. 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 h = 400 W/m".K and the junction thermo-physical properties are k = 20 W/m.K, c = 400 J/kg.K and p = 8500 kg/m³. 2 Leads T_ = 200°C h=400 W/m²K Gas stream TD Thermocouple k=20 W/m-K junction T₁ = 25°C c=400 J/kg-K p=8500 kg/m³ a) Determine the junction diameter needed for the thermocouple to have a thermal time constant T of 1s. Sphere volume: V=R³ and sphere area: A = 4πR² b) Using the diameter obtained in part a), calculate the Biot number and determine whether the thermocouple temperature can be assumed to be uniform.