Answer :
To find the absolute pressure when the gauge pressure of a gas is given, you follow these steps:
1. Understand the Terms:
- Gauge Pressure: This is the pressure of a system compared to the atmospheric pressure. It's the pressure reading you get from most pressure gauges, excluding the atmospheric pressure.
- Absolute Pressure: This is the total pressure measured from an absolute vacuum. It includes both the gauge pressure and the atmospheric pressure.
2. Use the Formula:
- The formula to calculate absolute pressure is:
[tex]\[
\text{Absolute Pressure} = \text{Gauge Pressure} + \text{Atmospheric Pressure}
\][/tex]
3. Given Values:
- The gauge pressure is [tex]\(114 \, \text{kPa}\)[/tex].
- The standard atmospheric pressure is [tex]\(101.3 \, \text{kPa}\)[/tex].
4. Calculate the Absolute Pressure:
[tex]\[
\text{Absolute Pressure} = 114 \, \text{kPa} + 101.3 \, \text{kPa} = 215.3 \, \text{kPa}
\][/tex]
5. Round to Closest Answer Choice:
- The exact calculation gives [tex]\(215.3 \, \text{kPa}\)[/tex], but since the answer choices provided don't have this specific value, look for the closest available correct option.
Based on the choices:
- The correct answer closest to [tex]\(215.3\)[/tex] is not directly listed, but the expected response should be evaluated carefully in context or potential rounding as [tex]\(214 \, \text{kPa}\)[/tex].
In this case, the closest accurate option seems to be a mismatch with provided choices, as none precisely matches due to the nature of rounding or descriptive omission in choices. If presenting, it must be introspected if all solutions are visible or if any resolution aligns contextual response accurately.
1. Understand the Terms:
- Gauge Pressure: This is the pressure of a system compared to the atmospheric pressure. It's the pressure reading you get from most pressure gauges, excluding the atmospheric pressure.
- Absolute Pressure: This is the total pressure measured from an absolute vacuum. It includes both the gauge pressure and the atmospheric pressure.
2. Use the Formula:
- The formula to calculate absolute pressure is:
[tex]\[
\text{Absolute Pressure} = \text{Gauge Pressure} + \text{Atmospheric Pressure}
\][/tex]
3. Given Values:
- The gauge pressure is [tex]\(114 \, \text{kPa}\)[/tex].
- The standard atmospheric pressure is [tex]\(101.3 \, \text{kPa}\)[/tex].
4. Calculate the Absolute Pressure:
[tex]\[
\text{Absolute Pressure} = 114 \, \text{kPa} + 101.3 \, \text{kPa} = 215.3 \, \text{kPa}
\][/tex]
5. Round to Closest Answer Choice:
- The exact calculation gives [tex]\(215.3 \, \text{kPa}\)[/tex], but since the answer choices provided don't have this specific value, look for the closest available correct option.
Based on the choices:
- The correct answer closest to [tex]\(215.3\)[/tex] is not directly listed, but the expected response should be evaluated carefully in context or potential rounding as [tex]\(214 \, \text{kPa}\)[/tex].
In this case, the closest accurate option seems to be a mismatch with provided choices, as none precisely matches due to the nature of rounding or descriptive omission in choices. If presenting, it must be introspected if all solutions are visible or if any resolution aligns contextual response accurately.
