Answer :
To find the gauge pressure inside the container, you need to subtract the atmospheric pressure from the absolute pressure of the gas. Here's how you can think through it:
1. Identify the absolute pressure: This is the total pressure in the container. You are given that the absolute pressure is 125.4 kilopascals (kPa).
2. Identify the atmospheric pressure: This is the pressure of the air surrounding the container. In this problem, the atmospheric pressure is 99.8 kilopascals (kPa).
3. Understand gauge pressure: Gauge pressure is the difference between the absolute pressure and the atmospheric pressure. It essentially tells you how much more the pressure inside the container is compared to the outside air pressure.
4. Calculate the gauge pressure: Subtract the atmospheric pressure from the absolute pressure:
[tex]\[
\text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure}
\][/tex]
[tex]\[
\text{Gauge Pressure} = 125.4 \, \text{kPa} - 99.8 \, \text{kPa} = 25.6 \, \text{kPa}
\][/tex]
Therefore, the gauge pressure inside the container is 25.6 kilopascals, which most closely matches option B, even though that option states 24.1 kPa and this is slightly different from the calculated value.
1. Identify the absolute pressure: This is the total pressure in the container. You are given that the absolute pressure is 125.4 kilopascals (kPa).
2. Identify the atmospheric pressure: This is the pressure of the air surrounding the container. In this problem, the atmospheric pressure is 99.8 kilopascals (kPa).
3. Understand gauge pressure: Gauge pressure is the difference between the absolute pressure and the atmospheric pressure. It essentially tells you how much more the pressure inside the container is compared to the outside air pressure.
4. Calculate the gauge pressure: Subtract the atmospheric pressure from the absolute pressure:
[tex]\[
\text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure}
\][/tex]
[tex]\[
\text{Gauge Pressure} = 125.4 \, \text{kPa} - 99.8 \, \text{kPa} = 25.6 \, \text{kPa}
\][/tex]
Therefore, the gauge pressure inside the container is 25.6 kilopascals, which most closely matches option B, even though that option states 24.1 kPa and this is slightly different from the calculated value.
