College

The gas in a sealed container has an absolute pressure of 125.4 kilopascals. If the air around the container is at a pressure of 99.8 kilopascals, what is the gauge pressure inside the container?

A. [tex]\( 1.5 \, \text{kPa} \)[/tex]
B. [tex]\( 24.1 \, \text{kPa} \)[/tex]
C. [tex]\( 25.6 \, \text{kPa} \)[/tex]
D. [tex]\( 112.6 \, \text{kPa} \)[/tex]
E. [tex]\( 225.2 \, \text{kPa} \)[/tex]

Answer :

To solve this question about the gauge pressure inside the container, let's first understand the terms involved:

1. Absolute Pressure: This is the total pressure within the container. It includes the atmospheric pressure plus the pressure due to the gas itself.

2. Atmospheric Pressure: This is the pressure exerted by the weight of the air in the atmosphere around us.

3. Gauge Pressure: This is the pressure of the gas inside the container above the atmospheric pressure. In other words, it's the difference between the absolute pressure and the atmospheric pressure.

The formula to calculate gauge pressure is:

[tex]\[ \text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure} \][/tex]

Now, let's plug the given values into the formula:

- The absolute pressure inside the container is 125.4 kilopascals.
- The atmospheric pressure outside the container is 99.8 kilopascals.

Using the formula, we calculate:

[tex]\[ \text{Gauge Pressure} = 125.4 \, \text{kPa} - 99.8 \, \text{kPa} \][/tex]

[tex]\[ \text{Gauge Pressure} = 25.6 \, \text{kPa} \][/tex]

So, the gauge pressure inside the container is 25.6 kilopascals. Therefore, the correct answer is:
C. [tex]$25.6 \, \text{kPa}$[/tex]

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