Calculating Air Column Length in a Capillary Tube Using Boyle's Law

In summary, the problem involves a uniform capillary tube with one sealed end that contains air trapped by a 40mm long mercury thread. When placed horizontally, the air column is 36mm long, but when placed vertically with the open end downwards, the air column is x mm in length. Using Boyle's law and assuming the air obeys it, we can calculate that x = 34.2 mm when the atmospheric pressure is 760 mmHg.
  • #1
Machodog
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Homework Statement


A uniform capillary tube (with one end sealed) contains air trapped by a mercury thread 40mm long. When the tube is placed horizontally, the length of the air column is 36 mm. When placed vertically, with the open end of the tube downwards, the length of air column is now x mm (the mercury is still 40mm).

Calculate x if the atmospheric pressure is 760 mmHg, assuming that the air obeys Boyle's law.

Homework Equations


Boyle's law, pV = constant.
density = mass/volume perhaps?

The Attempt at a Solution


I really have no clue how to start, any hints would be great.
 
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  • #2
The initial pressure of the air is 760 mm Hg. When placed vertically, the air pressure is 800 mm Hg. So the new length of the air column, according to Boyle's law is ##x=\frac{(760)(36)}{800}=34.2 mm##
 

What is fluid pressure?

Fluid pressure is the force exerted per unit area by a fluid, such as a liquid or gas, on the walls of its container. It is a result of the molecules of the fluid colliding with the walls and each other, creating a force that is evenly distributed throughout the container.

What factors affect fluid pressure?

The two main factors that affect fluid pressure are the density of the fluid and the depth or height of the fluid. As the density of the fluid increases, so does the pressure. Similarly, as the depth or height of the fluid increases, so does the pressure due to the weight of the fluid above.

How is fluid pressure measured?

Fluid pressure is typically measured using a device called a manometer, which consists of a U-shaped tube filled with a liquid, such as mercury or water. The height of the liquid in the tube is directly proportional to the pressure being exerted by the fluid being measured.

What is the difference between absolute and gauge pressure?

Absolute pressure is the total pressure exerted by a fluid, including atmospheric pressure. Gauge pressure is the difference between the absolute pressure and atmospheric pressure. Therefore, gauge pressure does not take into account the pressure of the surrounding air, while absolute pressure does.

How can fluid pressure be calculated?

Fluid pressure can be calculated using the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth of the fluid. This equation is known as the hydrostatic equation and is based on the principles of fluid mechanics.

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