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The compressed gas in a sealed container has a gauge pressure of 185.4 kilopascals. If the air around the container is at standard pressure, what is the
absolute pressure inside the container?



Answer :

GinnyAnswer
To find the absolute pressure inside the sealed container, you need to understand the difference between gauge pressure and absolute pressure. Gauge pressure refers to the pressure measured relative to the ambient or atmospheric pressure. Absolute pressure, on the other hand, includes the atmospheric pressure along with the gauge pressure.

Given:
- The gauge pressure inside the container is 185.4 kilopascals (kPa).
- The standard atmospheric pressure is 101.325 kilopascals (kPa).

### Step-by-Step Solution:

1. Identify the given values:
- Gauge pressure [tex]\(P_g\)[/tex] = 185.4 kPa
- Standard atmospheric pressure [tex]\(P_{atm}\)[/tex] = 101.325 kPa

2. Understand the relationship:
- Absolute pressure [tex]\(P_{abs}\)[/tex] is the sum of the gauge pressure [tex]\(P_g\)[/tex] and the atmospheric pressure [tex]\(P_{atm}\)[/tex].
Mathematically, this can be expressed as:
[tex]\[ P_{abs} = P_g + P_{atm} \][/tex]

3. Substitute the given values into the formula:
- [tex]\( P_{abs} = 185.4 \; \text{kPa} + 101.325 \; \text{kPa} \)[/tex]

4. Perform the addition:
- [tex]\( P_{abs} = 286.725 \; \text{kPa} \)[/tex]

### Conclusion:
The absolute pressure inside the container is [tex]\(286.725\)[/tex] kilopascals.

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