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

Answer:

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:

$\frac{P_{1}\times V_{1}}{T_{1}} = \frac{P_{2}\times V_{2}}{T_{2}}$

→ $V_{2} = \frac{P_{1}\times V_{1}\times T_{2}}{T_{1}\times P_{2}}$

→ $V_{2} = \frac{12.20 psi\times 33980.4 L\times 324.82 K}{294.26 K\times 102.2 psi}$

→ $V_{2} = 4477.63 L = 158.12 cf$

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