What is the gauge pressure of the gas in the closed tube in the figure? (Take the atmospheric pressure to be 76 cm Hg.)?

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BlackTom AI · Accepted Answer

To tackle this problem, first identify what is being asked: the gauge pressure of the gas in the closed tube, given atmospheric pressure is 76 cm Hg and the diagram shows a mercury difference of 20 cm between the two arms.
Option A: 200 mmHg. This corresponds to a gauge pressure of +200 mmHg, which would occur if the gas pressure is higher than atmospheric by 200 mmHg. If the gas pushes the mercury down on its side and the open arm is higher by 20 cm (200 mm), the gas side indeed experiences a pressure 200 mmHg above atmospheric. This makes sense as a positive gauge pressure.
Option B: 560 mm Hg. A value of 560 mmHg would imply a gross difference of 560 − 760 = −200 mmHg gauge relative to the air, or a situation where the gas pressure is actually lower than atmospheric by 560 − 760 = −200 mmHg, which corresponds to a negative gauge pressure of −200 mmHg. Since the diagram shows a clearly higher/lower mercury level suggesting a positive push from the gas, this does not fit typical gauge-pressure interpretation for a closed-end gas in this setup.
Option C: 260 mm Hg. Interpreting 260 mmHg as a gauge pressure would mean the gas pressure is 260 mmHg above atmospheric, i.e., P_gas ≈ 760 + 260 = 1020 mmHg. This would create a much larger mercury difference than shown (more than 20 cm), so it contradicts the given 20 cm (200 mm) difference in the figure.
Option D: 800 mm Hg. A gauge pressure of 800 mmHg would place P_gas at about 1560 mmHg, again far exceeding the 20 cm (200 mm) height difference depicted; this option implies a far greater shift than the diagram indicates and is inconsistent with the shown setup.
In summary, the only option that aligns with a 20 cm (200 mm) mercury height difference and a positive gauge pressure (gas pressure above atmospheric) is 200 mmHg.

SPHY001 Graded Quiz 6 (Unit 11 and Unit 12)- Requires Respondus LockDown Browser

What is the gauge pressure of the gas in the closed tube in the figure? (Take the atmospheric pressure to be 76 cm Hg.)?

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