Homework Question: A thermocouple junction of 1.0-mm in diameter is inserted in a large chamber to measure the temperature of hot gas flowing through the chamber. The hot gas has a velocity of 2 m/s and temperature (T) at 800 K. The chamber surface (T) is maintained at 500 K. (a) If the thermocouple is at room temperature, Ti when it is inserted in the chamber, calculate the time required for the temperature difference, (T.-T) to reach 2% of the initial temperature difference Ti-Ti. Neglect radiation and conduction through the leads. Properties of the thermocouple junction are approximated as k = 100W/m-K, c=385 J/kg.K and p = 8920 kg/m', while those of the hot gases may be assumed to have the properties of air at atmospheric pressure. (b) If the thermocouple junction has an emissivity of 0.5, what is the steady state temperature of the thermocouple junction? (c) The emissivity of the thermocouple junction can be controlled through application of a thin coating. How would changes in the emissivity affect the temperature measurement error? For emissivities in the range 0.1 SE SI, compute (i) the steady state junction temperature and (ii) the temperature measurement error. Results are to be presented in graphical and / or tabular forms and should be accompanied by substantial discussion supported by heat transfer fundamentals