Question

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.

Answer 1

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

Step-by-step 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:

`(P_(1)* V_(1))/(T_(1)) = (P_(2)* V_(2))/(T_(2))`

→
`V_(2) = (P_(1)* V_(1)* T_(2))/(T_(1)* P_(2))`

→
`V_(2) = (12.20 psi* 33980.4 L* 324.82 K)/(294.26 K* 102.2 psi)`

→
`V_(2) = 4477.63 L = 158.12 cf`

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