Question

Temperature 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

Answer 1

Concept:

Gauge pressure:

• Gauge pressure is the pressure relative to atmospheric pressure. Most of the pressure measuring devices are calibrated to read gauge pressure.
• P = ρgh

Atmospheric pressure:

• Atmospheric pressure or barometric pressure is the pressure within the atmosphere of Earth. Atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point.
• Patm = 1.013 bar.

Absolute pressure:

• Absolute pressure is the sum of gauge pressure and atmospheric pressure.
• Pabs = Pgauge + Patm .

The characteristic gas equation of an ideal gas is given by:

• ⇒ PV= mRT

Calculation:

GIven:

T = 288 K, V = 2 m3, h = 70 cm of mercury, R = 8314 J/kmol-K, P_atm = 1.01325 bar

Pressure p = ρgh = 0.7 × 13600 × 9.81 = 93391.2 Pa

P_actual = p_atm + p = 101325 + 93391.2 = 194716.2 Pa

And pv = mRT \(\Rightarrow m = \frac{{pv}}{{RT}}\)

\(\Rightarrow m = \frac{{194716.2 \times 2}}{{288 \times (\frac{8314}{28})}} = 4.5539\ kg\)