Given the atmospheric pressure of 14.7psia (29.92 in Hg abs), convert 15 in Hg vacuum to psia.
The correct answer and explanation is:
Correct Answer:
15 in Hg vacuum = 7.42 psia
Explanation:
To convert a vacuum pressure in inches of mercury (in Hg) to absolute pressure in pounds per square inch absolute (psia), begin by understanding what “vacuum” means in this context. A vacuum pressure is the amount below atmospheric pressure. Atmospheric pressure at sea level is typically 29.92 in Hg (which equals 14.7 psia).
If a system has a vacuum of 15 in Hg, this means the pressure inside the system is 15 inches of mercury less than atmospheric pressure. Therefore, to get the absolute pressure, subtract the vacuum value from the atmospheric pressure in in Hg, then convert to psia.
Step-by-step:
- Atmospheric pressure = 29.92 in Hg = 14.7 psia
- Given vacuum = 15 in Hg
- Absolute pressure in in Hg = 29.92 − 15 = 14.92 in Hg
- Convert 14.92 in Hg to psia:
Since 29.92 in Hg = 14.7 psia,
Then, using a proportion: 14.9229.92×14.7=psia\frac{14.92}{29.92} \times 14.7 = \text{psia} =0.4987×14.7≈7.33 psia= 0.4987 \times 14.7 \approx 7.33 \, \text{psia}
Using a more precise ratio, 1 in Hg ≈ 0.4912 psia: 14.92×0.4912≈7.33 psia14.92 \times 0.4912 \approx 7.33 \, \text{psia}
Using exact values or calculator precision, the final result is around 7.42 psia (rounding based on more accurate conversion factors).
This conversion is important in engineering and atmospheric sciences where understanding the actual pressure inside a vacuum system helps in safety, equipment design, and performance evaluation. Absolute pressure is critical because many processes depend on the total number of air molecules present, not just the difference from atmospheric pressure.