Height of Mercury in a pipe after removing it from a tub

In summary, the height of the residual column of Mercury in the pipe is 500 mm and the initial pressure of air in the head space is 1000 mm mercury.
  • #1
Balint
3
0

Homework Statement


We have a pipe open at both ends and having the length of 1 meter. After putting it into a tub of Mercury and thus filling it to the half, we close the upper end of it, and then remove it from the tub. What is the height of the residual column of the Mercury in the pipe?
pex=105 Pa

Homework Equations



The Attempt at a Solution


I don't even know where to start, as there is air inside the pipe at the beginning.
 
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  • #2
Hint: This will involve the use of the ideal gas law.
 
  • #3
I only know that the force that comes from the difference of the inner and outer pressure equals that of the Mercury column inside the pipe. But I don't know how to calculate with this as long as I don't have the density of Mercury, which I won't at the exam. Is that something I should learn or is there a way to get past that?

Here is my progress so far:
pV=nRT, since nRT is a constant, pV also is, so if I decrease pressure (or gravity does so) it will be ##\frac{p_0}{x}×V_0x=nRT##
As the diameter of the pipe is constant, I can use l instead of V, naturally only by itself, not in the ideal gas law, but that only helps me at the end.
Somehow ##\Delta p\sim F_u## and ##(1-Vx)\sim F_d##, but I don't know what to do next, as I would need a mass type multiplier somehow.
 
  • #4
Do you know the pressure in units of Torr (mmHg) ?
 
  • #5
I can convert it, I was given ##10^5 Pa##, that's 750,062 Torr, but I think he just wanted to make it easier to calculate in SI...
 
  • #6
1 torr = 1/760 atmosphere. Since 1 atmosphere is the pressure required to support a column of mercury to a height of 760 mm, I think you have a means to use the density of mercury without knowing the density of mercury.
 
  • #7
Balint said:
I only know that the force that comes from the difference of the inner and outer pressure equals that of the Mercury column inside the pipe. But I don't know how to calculate with this as long as I don't have the density of Mercury, which I won't at the exam. Is that something I should learn or is there a way to get past that?

Here is my progress so far:
pV=nRT, since nRT is a constant, pV also is, so if I decrease pressure (or gravity does so) it will be ##\frac{p_0}{x}×V_0x=nRT##
As the diameter of the pipe is constant, I can use l instead of V, naturally only by itself, not in the ideal gas law, but that only helps me at the end.
Somehow ##\Delta p\sim F_u## and ##(1-Vx)\sim F_d##, but I don't know what to do next, as I would need a mass type multiplier somehow.
You're on the right track. The initial height of the mercury in the column is 500 mm and 500 mm air. What is the initial pressure of air in the head space? Let 500+x be the final mm of air and 500-x be the final mm of mercury. In terms of x, what is the final mercury pressure at the top of the mercury column (in mm mercury)? In terms of x, what is the final air pressure in the head space (in mm mercury)? How do you think the air pressure in the head space is related to the mercury pressure at the top of the mercury column (i.e., at the exact same location)?
 

1. What is the purpose of removing mercury from a tub?

The purpose of removing mercury from a tub is typically to measure its height in a pipe. This can be done for various experiments and studies.

2. How is the height of mercury measured in a pipe?

The height of mercury in a pipe is typically measured using a ruler or measuring tape. The pipe should be held vertically and the height should be measured from the surface of the mercury to the top of the pipe.

3. Why is the height of mercury in a pipe important?

The height of mercury in a pipe is important because it can provide information about the properties and behavior of mercury. It can also be used to calculate the density of mercury and its interaction with other substances.

4. What factors can affect the height of mercury in a pipe?

The height of mercury in a pipe can be affected by changes in temperature, pressure, and the type of pipe used. It can also be influenced by the surface tension of mercury and any impurities present in the mercury.

5. Is there a standard height for mercury in a pipe after it is removed from a tub?

No, there is not a standard height for mercury in a pipe after it is removed from a tub. The height will vary depending on the amount of mercury used, the diameter and length of the pipe, and any external factors that may affect the height.

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