# How Much Air Is Needed to Lower Mercury in a Barometer from 75cm to 59cm?

In summary, the problem involves a barometer filled with mercury and a vacuum above it. The goal is to calculate the volume of air that would need to be introduced into the vacuum to lower the mercury column from 75cm to 59cm. The equations that can be used are Boyle's Law, pV = constant, and P = hρg. However, the question is unclear on whether the air should be pressurized or fit into a fixed volume while maintaining atmospheric pressure.

## Homework Statement

The mercury in a barometer of cross-sectional area 1cm square has a height of 75cm. There is vacuum above it, of length 9cm.

What is the volume of air, measured at atmospheric pressure, that would have to be admitted to cause the mercury column to drop to 59cm?

## The Attempt at a Solution

Should I use Boyle's Law, pV = constant?

Or Pressure = hpg? But problem is that I don't have the density of air?

Very confused, despite thinking for more than a day. Can anyone please kindly help?

If that's all that is given in the problem statement then I think it's fair to say you're working with room temp which should give you densities. When it asks how much air would need to be admitted is it saying into the vacuum to not make it a vacuum anymore?

abrewmaster said:
If that's all that is given in the problem statement then I think it's fair to say you're working with room temp which should give you densities. When it asks how much air would need to be admitted is it saying into the vacuum to not make it a vacuum anymore?

Thank you for the reply :)

Yes, you are right. Air is introduced into the empty space above the mercury, so that the empty space is no longer vacuum.

Ok, so you can calculate the change in pressure that would cause the mercury to move from 75cm to 59cm by using the equation you showed P=hρg. After finding that you can calculate how much air would be needed to go on top of it by using that same amount of pressure. The odd thing with how this question is worded is that it sounds like they want you to not pressurize the air but have it fill that fixed volume (because of the 9cm of vacuum above it) which at least initially seems impossible since air has such a smaller density than mercury but who knows. Is this the way the question was asked?

Edit: For clarity on my concern I mean that you have two fixed variables for the air that's being added. It has to fit in a defined volume yet also stay at a constant pressure (atmospheric) and you have to come up with how much volume would be needed? The question doesn't seem to make much sense.

I would first clarify the context in which this problem is being presented. Is it a homework question or a real-world scenario? This information can help determine the appropriate approach to finding a solution.

Assuming this is a homework question, I would suggest using Boyle's Law, as it relates pressure and volume at a constant temperature. In this case, the initial volume of air in the barometer is equal to the volume of the vacuum (which can be calculated using the given dimensions). The final volume can be calculated by using the new height of the mercury column (59cm) and the same cross-sectional area (1cm square). From there, you can solve for the pressure using the given atmospheric pressure and the ideal gas law (PV = nRT). Once you have the new pressure, you can use Boyle's Law to calculate the new volume of air needed to cause the mercury column to drop to 59cm.

If this is a real-world scenario, I would suggest using a different approach. Since the density of air is not given, you could assume standard conditions (1 atm and 273K) and use the ideal gas law to calculate the volume of air needed. However, this approach may not be entirely accurate since the atmospheric pressure and temperature may vary in different locations. In this case, it would be more appropriate to use a more precise instrument, such as a digital barometer, to measure the volume of air needed.

## What is a mercury barometer?

A mercury barometer is a scientific instrument used to measure air pressure. It consists of a long glass tube filled with mercury and inverted into a mercury-filled reservoir. The height of the mercury column in the tube is directly proportional to the atmospheric pressure.

## How does a mercury barometer work?

A mercury barometer works on the principle of atmospheric pressure. As the air pressure increases, it pushes down on the mercury in the reservoir, causing it to rise up the tube. The mercury column will stop rising once the weight of the mercury equals the weight of the air above it, indicating the air pressure at that location.

## What is the significance of using mercury in a barometer?

Mercury is a dense liquid, which makes it ideal for use in barometers. It is also non-reactive with air, allowing for accurate measurement of air pressure. However, due to its toxic nature, mercury barometers are being replaced by digital or aneroid barometers in many applications.

## What are the units of measurement for a mercury barometer?

The units of measurement for a mercury barometer are typically in inches of mercury (inHg) or millimeters of mercury (mmHg). These units indicate the height of the mercury column in the tube, which is directly related to the air pressure.

## What are the practical applications of a mercury barometer?

Mercury barometers are commonly used in meteorology to measure air pressure and predict weather patterns. They are also used in aviation and marine industries to monitor changes in air pressure that could affect flight or sea conditions. In addition, they are used in research and laboratory settings to study atmospheric pressure and its effects on various systems and materials.

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