A thermocouple shielded by aluminum foil of emissivity 0.15 is used to measure the temperature of hot gases flowing in a duct whose walls are maintained at T_w = 380 K. The thermometer shows a temperature reading of T_th = 530 K. Assuming the emissivity of the thermocouple junction to be ε = 0.7 and the convection heat transfer coefficient to be h = 120 W/m² · K, determine the actual temperature of the gas. What would the thermometer reading be if no radiation shield was used?

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Air wwwwwwwwww Thermocouple Tth = 530 K Tw= 380 K W