Question

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

Answer 1

Answer:

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