What is the Solution to the Mercury Barometer Problem?

In summary: So when the tube is inverted the pressure in the air bubble increases and the mercury column drops?Yes.
  • #1
utkarshakash
Gold Member
854
13

Homework Statement


To construct a barometer, a tube of length 1m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76cm. Suppose a 1m tube is filled with mercury up to 76cm and then closed by a cork. It is inverted in a mercury cup and the cork is removed. The height of mercury column in the tube over the surface in the
cup will be

a)zero b)76cm c)>76cm d)<76cm

Homework Equations



The Attempt at a Solution


Since the tube has been partially filled thus air is present in it. When it is inverted the air exerts a pressure on the mercury filled in it. Also the atm .pressure is exerted at the surface of mercury present in cup. But which one is greater?
 
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  • #2
The volume of the 24 cm column of air will probably increase once the tube is inverted.
 
  • #3
The next question is, to precisely what height will the mercury drop to?
 
  • #4
Basic_Physics said:
The volume of the 24 cm column of air will probably increase once the tube is inverted.

Why?
 
  • #5
The downwards pressure exected by the air and mercury column is balanced by the upwards atmospheric pressure.
 
Last edited:
  • #6
To answer the question in my previous post, you need to use the ideal gas law. You end up with the equation

100 - x + (24)(76)/x = 76

where x is the distance that the 24 cm increases to. The answer is x = 56.4 cm. That leaves a Hg column of 43.6 cm.
 
  • #7
Chestermiller said:
100 - x + (24)(76)/x = 76

.

Can you please make it more clear by stating what those numbers mean?
 
  • #8
utkarshakash said:
Can you please make it more clear by stating what those numbers mean?

The (100 - x) is the hydrostatic pressure of the Hg column in cm of Hg.

The (24)(76)/x is the pressure of the air bubble in cm of Hg. The 76 in this expression is the pressure of the air in the bubble before the bubble expands downward.

The pressure of the Hg column plus the pressure of the air bubble must equal the pressure of the atmosphere outside the tube at the Hg surface, which is equal to 76 cm of Hg.
 
  • #9
Chestermiller said:
.

The (24)(76)/x is the pressure of the air bubble in cm of Hg. The 76 in this expression is the pressure of the air in the bubble before the bubble expands downward.

Are you using PV=const equation?
 
  • #10
utkarshakash said:
Are you using PV=const equation?

Yes. Before the Hg level drops, the pressure in the air bubble is 76 cm Hg, and the length of the air bubble is 24 cm. If the area of the cylinder is A, the initial volume of the air bubble is 24A. After the Hg level drops, the length of the air bubble is x, and the volume of the air bubble is xA. So the volume ratio is (24A)/(xA). The new pressure in the expanded air bubble is

(76)(24A)/(xA) = (76)(24)/x cm Hg.
 
  • #11
Chestermiller said:
Yes. Before the Hg level drops, the pressure in the air bubble is 76 cm Hg, and the length of the air bubble is 24 cm. If the area of the cylinder is A, the initial volume of the air bubble is 24A. After the Hg level drops, the length of the air bubble is x, and the volume of the air bubble is xA. So the volume ratio is (24A)/(xA). The new pressure in the expanded air bubble is

(76)(24A)/(xA) = (76)(24)/x cm Hg.

OK I have understood.
 

Related to What is the Solution to the Mercury Barometer Problem?

1. What is a mercury barometer?

A mercury barometer is a scientific instrument used to measure atmospheric pressure. It consists of a long glass tube filled with mercury and inverted in a dish of mercury. As the atmospheric pressure changes, the level of mercury in the tube also changes, allowing for the measurement of pressure.

2. How does a mercury barometer work?

A mercury barometer works on the principle that atmospheric pressure can support a column of mercury. As the atmospheric pressure increases, it pushes down on the surface of the mercury in the dish, causing it to rise in the tube. The height of the mercury column in the tube is directly proportional to the atmospheric pressure.

3. What is the purpose of a mercury barometer?

The purpose of a mercury barometer is to measure changes in atmospheric pressure. This information is important for weather forecasting, as changes in atmospheric pressure can indicate upcoming weather patterns. It is also used in scientific research and in the calibration of other instruments.

4. What are the advantages of a mercury barometer?

Mercury barometers have a high level of accuracy and precision, making them a reliable tool for measuring atmospheric pressure. They are also relatively simple in design and can be easily calibrated. Additionally, mercury is a dense liquid, so a relatively small amount can be used to measure high pressures.

5. What are the potential dangers of a mercury barometer?

Mercury is a toxic substance and can be harmful if it comes into contact with the skin or is ingested. It is also a volatile liquid, meaning it can evaporate and release toxic fumes. Due to these hazards, the use of mercury barometers has decreased and alternative methods for measuring atmospheric pressure have been developed.

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