# What Will The Density Be If The Radius Of The Sphere Is Halved, Compressing The Air Within?

• Puzzle

When it comes to designing, engineering, and constructing buildings, structures, and even cities, one of the most important factors to consider is density.

How dense a material is determines how it can be used. For example, a very dense metal such as tungsten may be used to make a bulletproof window since it is hard to penetrate. A less dense wood may be used to build floors or structures due to its softness.

When talking about density in cities, the term usually refers to the number of people living in a particular area. A densely populated area has lots of people living there which leads to many opportunities and activities. There are lots of shops and services available due to the demand for them.

This article will talk about another type of density: atmospheric density. This refers to the amount of pressure exerted on the surface of a sphere by the air inside it.

## Compress the air to half the radius

Now let’s try something a little more difficult. Suppose you have a sphere with a certain radius, and you compress the air within it to half the radius. What will the density of the air be?

The volume of the air inside will be reduced by half, so to keep the same volume of air, you must increase the pressure. The pressure will depend on how you increase it—whether you use a higher pressure source or add more gas to the sphere.

If you use a higher-pressure source, then the density will not change. The number of molecules per unit volume will stay the same, but there will be more force pushing them apart. If you add more gas to the sphere, then there will be more molecules in that unit volume, so its density will go up.

## What happens to the air?

As the radius of the sphere is halved, the amount of space occupied by the air within the sphere is also halved. This means that the air is compressed, and each molecule of air comes into contact with more particles of other gases.

Because there are more collisions, there is less space between molecules. The pressure of the air also increases, as it is pushed down by surrounding molecules.

The strength of this pressure increase depends on how many molecules are in contact and how hard they push down. Because there are more collisions and less space between molecules, the density increases.

You can try this at home with a bottle of water: Put half a bottle of water in a tight bag, then compress the bag until it is half as tall.

## What happens to the temperature?

To understand how temperature is affected by compression, consider what happens when a given volume of air is compressed into a smaller volume.

You can think of air as a combination of three things: nitrogen, oxygen, and very small amounts of other gases. All of these substances have mass, and all have corresponding volumes.

When air is compressed, the total mass doesn’t change. So if there’s a certain amount of mass per volume, then compressing that volume will result in the same mass per unit area.

What does change is the ratio of surface area to volume. This ratio gets smaller as the volume gets smaller. There’s less space between the molecules on the outside and inside, for instance.

So what happens when air is compressed? The mass per unit area stays the same, but the surface area per unit volume decreases. That means there’s less space for the molecules to be in.

## What is the new density?

If the radius of the sphere is halved, compressing the air within, then the new density of air will be twice as heavy. This is because there are twice as many molecules in a given volume of air.

In other words, there will be twice as many molecules per cubic meter. Since one cubic meter of air weighs one kilogram, the total weight of the air will double.

If you were able to compress air down to a single point, called a singularity, then all of the air in the world would fit into an infinitely small point. There would be an infinite amount of pressure on every surface surrounding this point, with no escape.

This is because there is an infinite number of atoms and there is no way to reduce their distance between each other.

## Is this a realistic scenario?

Yes, this is a very realistic scenario. As mentioned before, supercompression occurs in almost all substances. Most of the time, we are not able to reduce the size of the object enough to where it compresses its contents enough to double (or more) its density.

For example, it would be difficult to compress a soccer ball sized glob of water enough to turn it into a small, heavy cube of water. We would need very high pressure and/or very little volume to do this!

With most substances, supercompression occurs due to mutual interconnection between parts of the substance. For example, if you were able to pull out individual molecules of a substance and lay them end-to-end, then they would be able to interact and entangle with other similar molecules, thus possibly preventing any compression from occurring.

This is why when trying to supercompress a material, it is important to use very fine particles of the substance in order to prevent any mutual interconnection between parts of the material.

## What are the limitations of this scenario?

In this scenario, you can only compress the air within the sphere until it reaches its first limiting factor: the density of the material of the sphere itself.

As mentioned before, air is composed of molecules, mainly nitrogen and oxygen. These molecules are extremely lightweight due to their small size and lack of weight-bearing factors.

Because of this, it is very hard to compress air molecules into a smaller space. To do so would require incredible force, which would ultimately take a lot of energy.

The second limiting factor in compressing air within a sphere is the ratio between the pressure inside and outside of the sphere. As mentioned before, if you were to compress the air down into a denser space, it would result in higher pressure inside of the sphere. This would cause issues with keeping an intact barrier between inside and outside of the sphere.

## Is there another way to compress air?

Yes! Pressurizing air can be done through various methods, one of the most common being pumping air into a space with a device.

Air can also be pressurized by stirring up the air molecules, creating friction that increases its density. This is how wind turbines work, for example.

You can also pressurize air by freezing it, which adds volume due to the expanded molecular structure. Ice is less dense than liquid water, after all!

You could even try compressing the air inside a sphere down to half its radius, and the density will remain the same. The air will just be more crowded and compressed within the sphere.

This is because compression of gases only reduces volume if there is some kind of barrier between molecules or particles of the gas. Otherwise, it does not change its density.

## How can I use this in my writing?

This question can be applied to many things in your writing. How can your characters be more intimate? How can your story be more compact? How can your setting be more vivid?

The answers to all of these questions lie in compressing the relevant elements of your story. By making your characters less intimate, you make the conflict between them more apparent; by making your story less compact, you make the layers and twists more obvious; by making the setting less vivid, you emphasize other elements that are planted within it.

All of these create deeper understanding of what is happening in the story.

You can also apply this question to ask: What if the density of a substance is halved? Will it still have the same effect? The answer is no—it will not.

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