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A spherical thermocouple junction 1.0 mm in diameter is inserted in a combustion chamber to measure the temperature T∞​ of the products of combustion. The hot gases have a velocity of V=20 m/s. (a) If the thermocouple is at room temperature, Ti​, when it is inserted in the chamber, estimate the time required for the temperature difference, T∞​−T, to reach 2% of the initial temperature difference, T∞​−Ti​. Neglect radiation and conduction through the leads. Properties of the thermocouple junction are approximated as k=100 W/m⋅K,c=385 J/kg⋅K, and ρ=8920 kg/m3, while those of the combustion gases may be approximated as k=0.05 W/m⋅K,ν=50×10−6 m2/s, and Pr=0.69. (b) If the thermocouple junction has an emissivity of 1.0 and the cooled walls of the combustor are at Tc​=400 K, what is the steadystate temperature of the thermocouple junction if the combustion gases are at 1000 K ? Conduction through the lead wires may be neglected.