Consider temperature measurement in a gas stream using the thermocouple junction described in Problem 7.66 ( \(D=2 \mathrm{~mm}, \varepsilon=0.60\) ). If the gas velocity and temperature are \(2 \mathrm{~m} / \mathrm{s}\) and \(500^{\circ} \mathrm{C}\), respectively, what temperature will be indicated by the thermocouple if the duct surface temperature is \(350^{\circ} \mathrm{C}\) ? The gas may be assumed to have the properties of atmospheric air. What temperature will be indicated by the thermocouple if the gas pressure is doubled and all other conditions remain the same?

Data From Problem 7.66:-

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 \(T_{s}\) 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-mmdiameter sphere with a surface emissivity of 0.60 is placed in a gas stream moving at \(3 \mathrm{~m} / \mathrm{s}\). If the thermocouple senses a temperature of \(320^{\circ} \mathrm{C}\) when the duct surface temperature is \(175^{\circ} \mathrm{C}\), 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 \(1 \leq V \leq 25 \mathrm{~m} / \mathrm{s}(\varepsilon=0.6)\) and for emissivities in the range \(0.1 \leq \varepsilon \leq 1.0(V=3 \mathrm{~m} / \mathrm{s})\).

Transcribed Image Text:

Duct Hot gases T Thermocouple junction