A thermocouple junction is inserted in a large duct to measure the temperature of hot gases flowing through the duct.

(a) If the duct surface temperature Ts is less than the gas temperature T_g, will the thermocouple sense a temperature that is less than, equal to. or greater than T_g? Justify your answer on the basis of a simple analysis.

(b) A thermocouple junction in the shape of a 2-mm-diameter sphere with a surface emissivity of 0.60 is placed in a gas stream moving at 3 m/s. If the thermocouple senses a temperature of 320°C when the duct surface temperature is 175°C, what is the actual gas temperature? The gas may be assumed to have the properties of air at atmospheric pressure.

(c) How would changes in velocity and emissivity affect the temperature measurement error? Determine the measurement error for velocities in the range 1 < V < 25 m/s (ε = 0.6) and for emissivities in the range 0.1 < ε < 1.0 (V = 3 m/s).

T, 7 Duct Hot gases Thermocouple junction