A cylinder of 50-litre capacity contains oxygen at temperature of 27°C and at absolute pressure 10 MPa. What will be the density of oxygen? [Gas constant for oxygen is 0.26 kJ/kg-K]

Concept:

A hypothetical gas that obeys the law PV = nR̅T at all pressures and temperatures is called Ideal gas. There are two equations for Ideal Gas.

• PV = nR̅T
• PV = mRT, P = ρRT

where,

P = Absolute pressure (Pa), V = Volume (m³), n = Number of moles of the gas \( = \frac{{\bf{m}}}{{\bf{M}}}\)

\({\bar{R}} = \;\)Universal gas constant (8314 J/kg-mol.K), T = Absolute Temperature (K)

\(R = characteristic\;gas\;constant = \frac{{\bar R}}{M}\;\left( {\frac{J}{{kg.K}}} \right)\), M = Molecular weight of the gas

m = Mass of gas (kg) & ρ = Density of gas (kg/m³)

[Note: Use any of the above equation as per the inputs given]

Calculation:

Given:

V = 50 lit, T = 27 °C ⇒ 300 K, P_abs = 10 MPa ⇒ 10 × 10⁶ Pa, R = 0.26 kJ/kg-K ⇒ 0.26 × 10³ J/kg-K

∵ P = ρRT 

⇒ 10 × 10⁶ = ρ × 0.26 × 10³ × 300 

⇒ ρ = 128.20 kg/m³