Assuming Ideal Gas Law is applicable, calculate density, specific weight, and specific volume of air at 120 oF and 50 psia.

a) ρ = 3.735 Kg/m³

b) γ = 36.603 N/m³

c) Vw = 2.68 E-4 g/m³

Explanation:

PV = RTn ... ideal gas law

a) ρ = m/V

∴ Mw air = 28.966 g/mol ... from literature

⇒ P = RTn / V

∴ n = m / Mw

⇒ P = mRT / Mw. V = m/V * R. T/Mw

ρ = P. Mw / R. T

∴ P = 50 psi = 344738 Pa

∴ R = 8.3144 Pa. m³/mol. K

∴ T = 120°F = 48.889 °C = 321.889 K

⇒ ρ = ((344738 Pa) * (28.996 g/mol)) / ((8.3144 Pa. m³/mol. K) * (321.889K))

⇒ ρ = 3734.996 g/m³ * (Kg / 1000g) = 3.735 Kg/m³

specific weight:

γ = w / V = m. g / V = ρ * g

∴ ρ = 3.735 Kg/m³

∴ g = 9.8 m/s²

⇒ γ = 36.603 N/m³

c) specific volume

Vw = R. T / P. Mw

⇒ Vw = ((8.3144 Pa. m³ / mol. K) * (321.889 K)) / (344738 Pa) * (28.966 g/mol)

⇒ Vw = 2.68 E-4 g/m³