An air compressor draws in 1,200 cf of free air at a gauge pressure of 0 psi and a temperature of 70°f. the air is compressed to a gauge pressure of 90 psi at a temperature of 125°f. the atmospheric pressure is 12.20 psi. determine the volume of air after it is compressed.

The final volume of air after compression: V₂ = 4477.63 L = 158.12 cf

Explanation:

Given: Initial gauge pressure of the gas = 0 psi

Initial absolute pressure of the gas: P₁ = gauge pressure + atmospheric pressure = 0 psi + 12.20 psi = 12.20 psi

Initial Temperature = 70°F

⇒ T₁ = (70°F − 32) × 5/9 + 273.15 = 294.26 K

Initial volume of the gas: V₁ = 1200 cf = 1200 × 28.317  = 33980.4 L    (∵ 1 cf ≈ 28.317  L)

Final gauge pressure of the gas = 90 psi

Final absolute pressure of the gas: P₂ = gauge pressure + atmospheric pressure = 90 psi + 12.20 psi = 102.2 psi

Final Temperature: T₂ = 125°F

⇒ T₂ = (125°F − 32) × 5/9 + 273.15 = 324.82 K

Final volume of the gas: V₂ = ? L      

According to the Combined gas law:

→

→

→

Therefore, the final volume of air after compression: V₂ = 4477.63 L = 158.12 cf