Determining the Level of Mercury in U shaped tube

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SUMMARY

The discussion focuses on calculating the height of mercury (L) in a U-shaped tube filled with air at 293K and 1 atm, where mercury is poured in without allowing air to escape. The relevant equations include the ideal gas law (PV=NRT) and the hydrostatic pressure equation (P=P_0 + pgd). Participants emphasize the need to relate the air pressure to the mercury pressure, considering that the air pressure will equal the pressure exerted by the mercury column on the opposite side of the tube.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=NRT)
  • Knowledge of hydrostatic pressure principles (P=P_0 + pgd)
  • Familiarity with pressure units conversion (1 atm = 760 mmHg)
  • Basic concepts of fluid mechanics and density
NEXT STEPS
  • Explore the relationship between gas pressure and fluid height in U-tubes
  • Study the implications of compressible vs. incompressible fluids in pressure calculations
  • Learn about the effects of temperature on gas volume and pressure
  • Investigate advanced applications of hydrostatic pressure in engineering contexts
USEFUL FOR

Students in physics or engineering courses, particularly those studying fluid mechanics and thermodynamics, as well as educators looking for practical examples of pressure calculations in U-shaped tubes.

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Homework Statement



A u shaped tube has a total length of 1 m, it is initially filled with air at 293K and 1 atm, mercury is poured in without letting air escape, compressing the air. This continues until the mercury is filled to a level L, how long is L

The tube is open at one end, closed at the other

Homework Equations


We have PV=NRT, P=P_0 +pgd


The Attempt at a Solution


Obviously I have to relate the air levels to that of mercury, as well as relating pressures, 1 atm = 760 mmHG so there is that, but its no longer at 1 atm. Someone want to give me a hint here? I am not looking for the answer just some insight. Everything I can think of deals with the area or the density
 
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The air pressure must equal the pressure of the mercury at its surface in contact with the air. The pressure of the mercury will be the weight of the column of mercury on the other side of the tube, above that contact surface, divided by the surface area.
 

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