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:

a) ρ = m/V

∴ Mw air = 28.966 g/molfrom literature

⇒  P = RTn / V

∴ n = m / Mw

⇒ P = mRT / Mw.V = m/V * R.T/Mw

∴ 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:

∴ ρ = 3.735 Kg/m³

∴ g = 9.8 m/s²

⇒ γ = 36.603 N/m³

c) specific volume

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

⇒ Vw = 2.68 E-4 g/m³

a

explanation:

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j