To determine the gauge pressure inside the container, we need to understand the difference between absolute pressure and gauge pressure.
1. Absolute Pressure is the total pressure exerted on the gas, including the atmospheric pressure plus the gauge pressure.
2. Gauge Pressure is the pressure of the gas inside the container above the atmospheric pressure. It is the pressure read on a gauge that measures pressure relative to the atmospheric pressure.
Given:
- Absolute pressure ([tex]\(P_{abs}\)[/tex]) = 9.25 atmospheres
- Standard atmospheric pressure ([tex]\(P_{atm}\)[/tex]) = 1 atmosphere (by definition)
The relationship between absolute pressure, gauge pressure ([tex]\(P_{gauge}\)[/tex]), and atmospheric pressure is:
[tex]\[ P_{abs} = P_{gauge} + P_{atm} \][/tex]
To find the gauge pressure, we rearrange the equation:
[tex]\[ P_{gauge} = P_{abs} - P_{atm} \][/tex]
Substituting the given values:
[tex]\[ P_{gauge} = 9.25 \, \text{atm} - 1 \, \text{atm} \][/tex]
[tex]\[ P_{gauge} = 8.25 \, \text{atm} \][/tex]
Therefore, the gauge pressure inside the container is [tex]\(8.25 \, \text{atm}\)[/tex].
The correct answer is:
B. 8.25 atm
