Project ForgeA gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section at 100 kPa and 27°C with a volume flow rate of 15 m³/s. If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is (constant pressure, ideal gas, negligible KE/PE change, constant specific heat; Cp=1 kJ/kg·K, R=0.5 kJ/kg·K)
- 32°C
- B37°C
- C53°C
- D76°C
Explanation
Mass flow rate from the ideal gas law: ṁ = pV̇/(RT) = (100×15)/(0.5×300) = 10 kg/s. Net heat added = 101−51 = 50 kW. From SFEE, Q_net = ṁ Cp ΔT → ΔT = 50/(10×1) = 5°C. Exit temperature = 27+5 = 32°C.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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