Project ForgeTemperature of nitrogen in a vessel of volume 2 m³ is 288 K. A U-tube manometer connected to the vessel shows a reading of 70 cm of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325 bar, acceleration due to gravity is 9.81 m/s² and density of mercury is 13600 kg/m³. The mass of nitrogen (in kg) in the vessel is __________.
Explanation
Gauge pressure from the manometer = ρ_Hg·g·h = 13600×9.81×0.70 ≈ 93,406 Pa. Absolute pressure = 101,325+93,406 ≈ 194,731 Pa. Specific gas constant for N2 (M=28 kg/kmol): R = 8314/28 ≈ 296.9 J/kg-K. Mass = PV/(RT) = 194,731×2/(296.9×288) ≈ 4.56 kg.
Source: GATE ME 2015 (Session 1) (2015)
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