To determine the gauge pressure inside the container, we need to understand the relationship between absolute pressure, gauge pressure, and standard atmospheric pressure.
1. Absolute Pressure (Pabs): This is the total pressure within the container, which is the sum of the atmospheric pressure and the gauge pressure.
2. Standard Atmospheric Pressure (Patm): This is the pressure exerted by the Earth's atmosphere at sea level and is conventionally taken as 1 atmosphere (atm).
3. Gauge Pressure (Pgauge): This is the pressure within the container above and beyond the atmospheric pressure.
The relationship is given by:
[tex]\[ P_{\text{abs}} = P_{\text{gauge}} + P_{\text{atm}} \][/tex]
We are given the absolute pressure inside the container and the standard atmospheric pressure:
- Absolute pressure, [tex]\( P_{\text{abs}} = 9.25 \)[/tex] atmospheres
- Standard atmospheric pressure, [tex]\( P_{\text{atm}} = 1 \)[/tex] atmosphere
We need to find the gauge pressure, which can be rearranged from the above formula:
[tex]\[ P_{\text{gauge}} = P_{\text{abs}} - P_{\text{atm}} \][/tex]
Substituting the given values:
[tex]\[ P_{\text{gauge}} = 9.25 \, \text{atm} - 1 \, \text{atm} \][/tex]
[tex]\[ P_{\text{gauge}} = 8.25 \, \text{atm} \][/tex]
Therefore, the gauge pressure inside the container is [tex]\( 8.25 \)[/tex] atmospheres.
The correct answer is:
B. 8.25 atm
