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:
[tex]\frac{P_{1}\times V_{1}}{T_{1}} = \frac{P_{2}\times V_{2}}{T_{2}}[/tex]
→ [tex]V_{2} = \frac{P_{1}\times V_{1}\times T_{2}}{T_{1}\times P_{2}}[/tex]
→ [tex]V_{2} = \frac{12.20 psi\times 33980.4 L\times 324.82 K}{294.26 K\times 102.2 psi}[/tex]
→ [tex]V_{2} = 4477.63 L = 158.12 cf [/tex]
Therefore, the final volume of air after compression: V₂ = 4477.63 L = 158.12 cf
