To determine the gauge pressure inside the container, first understand the difference between absolute pressure and gauge pressure.
1. Absolute Pressure: This is the total pressure exerted on the walls of a container, including atmospheric pressure. Here, the absolute pressure in the sealed container is given as [tex]\( 9.25 \)[/tex] atmospheres.
2. Standard Atmospheric Pressure: This is the average pressure exerted by the earth's atmosphere at sea level, which is given as [tex]\( 1 \)[/tex] atmosphere.
3. Gauge Pressure: This is the pressure relative to the atmospheric pressure. It can be calculated by subtracting the atmospheric pressure from the absolute pressure.
Formally, the relationship can be written as:
[tex]\[ \text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure} \][/tex]
Given:
[tex]\[ \text{Absolute Pressure} = 9.25 \, \text{atm} \][/tex]
[tex]\[ \text{Atmospheric Pressure} = 1 \, \text{atm} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ \text{Gauge Pressure} = 9.25 \, \text{atm} - 1 \, \text{atm} \][/tex]
Perform the subtraction:
[tex]\[ \text{Gauge Pressure} = 9.25 \, \text{atm} - 1 \, \text{atm} = 8.25 \, \text{atm} \][/tex]
The gauge pressure inside the container is [tex]\( \boxed{8.25 \, \text{atm}} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \mathbf{B. \, 8.25 \, \text{atm}} \][/tex]
