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Answer :
To find the pressure of the gas sample in the open-end manometer question, follow these steps:
1. Understand the problem: The atmospheric pressure is given as 103.4 kPa, and the mercury level is 46.0 mm lower on the atmosphere side. This means that the gas in the manometer has a higher pressure than the atmospheric pressure by this difference in mercury levels.
2. Convert the mercury level difference to pressure units:
- The difference in mercury level is given in millimeters (mm). To convert this to kilopascals (kPa), we need to know that 1 mmHg (millimeter of mercury) is approximately equal to 0.133322 kPa.
3. Calculate the difference in pressure due to mercury level:
- Multiply the mercury level difference by the conversion factor:
[tex]\[
46.0 \, \text{mm} \times 0.133322 \, \text{kPa/mm} = 6.1328 \, \text{kPa}
\][/tex]
4. Determine the gas pressure:
- Since the mercury level is lower on the atmospheric side, it implies that the gas pressure is higher than the atmospheric pressure.
- Add the pressure difference to the atmospheric pressure to find the gas pressure:
[tex]\[
103.4 \, \text{kPa} + 6.1328 \, \text{kPa} = 109.5328 \, \text{kPa}
\][/tex]
5. Select the correct answer:
- From the given choices, the pressure of the gas sample, 109.5 kPa, corresponds to option c. 109.5 kPa.
Thus, the pressure of the gas sample is 109.5 kPa.
1. Understand the problem: The atmospheric pressure is given as 103.4 kPa, and the mercury level is 46.0 mm lower on the atmosphere side. This means that the gas in the manometer has a higher pressure than the atmospheric pressure by this difference in mercury levels.
2. Convert the mercury level difference to pressure units:
- The difference in mercury level is given in millimeters (mm). To convert this to kilopascals (kPa), we need to know that 1 mmHg (millimeter of mercury) is approximately equal to 0.133322 kPa.
3. Calculate the difference in pressure due to mercury level:
- Multiply the mercury level difference by the conversion factor:
[tex]\[
46.0 \, \text{mm} \times 0.133322 \, \text{kPa/mm} = 6.1328 \, \text{kPa}
\][/tex]
4. Determine the gas pressure:
- Since the mercury level is lower on the atmospheric side, it implies that the gas pressure is higher than the atmospheric pressure.
- Add the pressure difference to the atmospheric pressure to find the gas pressure:
[tex]\[
103.4 \, \text{kPa} + 6.1328 \, \text{kPa} = 109.5328 \, \text{kPa}
\][/tex]
5. Select the correct answer:
- From the given choices, the pressure of the gas sample, 109.5 kPa, corresponds to option c. 109.5 kPa.
Thus, the pressure of the gas sample is 109.5 kPa.
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