A thermocouple whose surface is diffuse and gray with an emissivity of 0.6 indicates a temperature of

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A thermocouple whose surface is diffuse and gray with an emissivity of 0.6 indicates a temperature of 180°C when used to measure the temperature of a gas flowing through a large duct whose walls have an emissivity of 0.85 a uniform temperature of 450℃.

(a) If the convection heat transfer coefficient between the thermocouple and the gas stream is h̅ = 125 W/m². K and there are negligible conduction losses from the thermocouple, determine the temperature of the gas.

(b) Consider a gas temperature of 125°C. Compute and plot the thermocouple measurement error as a function of the convection coefficient for 10 < h̅ < 1000 W/m². K. What are the implications of your results?

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