Answer :
To determine the absolute pressure of a gas when you know the gauge pressure, you need to consider the atmospheric pressure as well. Here's a step-by-step explanation of how this works:
1. Understand the Definitions:
- Gauge Pressure: This is the pressure of the gas relative to atmospheric pressure. It excludes atmospheric pressure.
- Atmospheric Pressure: Typically, this is approximately 101.3 kPa at sea level.
- Absolute Pressure: This is the total pressure exerted by the gas, including the atmospheric pressure.
2. Calculate the Absolute Pressure:
- The formula for absolute pressure is:
[tex]\[
\text{Absolute Pressure} = \text{Gauge Pressure} + \text{Atmospheric Pressure}
\][/tex]
3. Apply the Given Values:
- Given the gauge pressure is 114 kPa and the standard atmospheric pressure is about 101.3 kPa, you can calculate:
[tex]\[
\text{Absolute Pressure} = 114 \, \text{kPa} + 101.3 \, \text{kPa} = 215.3 \, \text{kPa}
\][/tex]
4. Identify the Closest Answer:
- Among the options given: 14 kPa, 214 kPa, 50 kPa, and 220 kPa, the closest to 215.3 kPa is 214 kPa.
Therefore, the absolute pressure of the gas is approximately 214 kPa. So, the correct answer is B) 214 kPa.
1. Understand the Definitions:
- Gauge Pressure: This is the pressure of the gas relative to atmospheric pressure. It excludes atmospheric pressure.
- Atmospheric Pressure: Typically, this is approximately 101.3 kPa at sea level.
- Absolute Pressure: This is the total pressure exerted by the gas, including the atmospheric pressure.
2. Calculate the Absolute Pressure:
- The formula for absolute pressure is:
[tex]\[
\text{Absolute Pressure} = \text{Gauge Pressure} + \text{Atmospheric Pressure}
\][/tex]
3. Apply the Given Values:
- Given the gauge pressure is 114 kPa and the standard atmospheric pressure is about 101.3 kPa, you can calculate:
[tex]\[
\text{Absolute Pressure} = 114 \, \text{kPa} + 101.3 \, \text{kPa} = 215.3 \, \text{kPa}
\][/tex]
4. Identify the Closest Answer:
- Among the options given: 14 kPa, 214 kPa, 50 kPa, and 220 kPa, the closest to 215.3 kPa is 214 kPa.
Therefore, the absolute pressure of the gas is approximately 214 kPa. So, the correct answer is B) 214 kPa.
