Exhaust gases having properties similar to dry air enter an exhaust stack at 800 K. The stack is made of steel and is 8 m tall and 0.5 m ID. The gas flow rate is 0.5 kg/s and the ambient temperature is 280 K. The outside of the stack has an emissivity of 0.9. If heat loss from the outside is by radiation and natural convection, calculate the gas outlet temperature.GIVENExhaust gas flow through a steel stackExhaust gas has the properties of dry airEntering exhaust temperature (Tb,in) = 800 KStack height (L) = 8 mStack diameter (D) = 0.5 mGas flow rate (m)= 0.5 kg/sAmbient temperature (T??) = 280 KStack emissivity (ε) = 0.9ASSUMPTIONSSteady stateThe surrounding behave as a black body enclosure at the ambient temperatureThermal resistance of the duct is negligibleDuct thickness isnegligible

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Taout =? T=280 K Tan- 800 K Exhaust Gas m-0.5 kg/s w g'o-a L=8 m