# Why is denser air heavier than less dense air?

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It does not become lighter in the sense of less massive, rather it expands to take up more volume. The principle of buoyancy (since we are immersed in an atmosphere) then makes it appear lighter.

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The air expands as heated becauses the average separation of the gas molecules get larger at higher temperature. Hence, there are less gas molecules per unit volume, that is the reason why the it is lighter or density is smaller.

The website is trying to explain the process of the mechanism of vertical motion of atmosphere caused by adiabatic expansion or shrinkage. There are basically two modes:

When the air is near the ground, it is heated and it rise up because it is less dense than that of cold air. During the process of rising, it expands more as the pressure is smaller, then it gets cooled. This called adiabatic cooling. The reverse process occurs on the cold air.

You can refer to the ideal gas law and the for basic process of the ideal gas: isothermal(constant T),isobaric(constant P),adiabatic/isotropic(Q=0/constant S) and isochoric(constant V) process. The following link may help you.

http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html

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It does not become lighter in the sense of less massive, rather it expands to take up more volume. The principle of buoyancy (since we are immersed in an atmosphere) then makes it appear lighter.

So if there was no atmosphere like on the Moon then denser air will not be lighter than less dense air?

Merged post follows:

Consecutive posts merged
The air expands as heated becauses the average separation of the gas molecules get larger at higher temperature. Hence, there are less gas molecules per unit volume, that is the reason why the it is lighter or density is smaller.

What I don't get is that by density we mean mass per unit volume but when we say 'lighter' we actually mean 'weights less or of less weight'. So why does less mass per unit volume mean less weight?

Edited by Uri
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So if there was no atmosphere like on the Moon then denser air will not be lighter than less dense air?

Assuming the same mass of air they would weigh the same on the moon.

Assuming the same volume the denser air would weigh more due to the additional mass in the same volume.

No atmosphere means no buoyant forces to complicate matters.

Most would say less dense air is lighter generally, but it depends on what you are comparing and what you mean by lighter.

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Less dense air is going to have less mass (and therefore less weight) per unit volume, yeah. That's what "less dense" means. A mass of air that is less dense than the air around it is going to rise up, because the denser, heavier air around it is going to be pulled down more and force the less dense air up and out of the way. That's buoyancy.

Think about a rock dropped into the ocean. Sure, obviously, the ocean is heavier than the rock. But the rock is heavier per unit volume, so it sinks.

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Assuming the same mass of air they would weigh the same on the moon.

Assuming the same volume the denser air would weigh more due to the additional mass in the same volume.

I still don't get it. Why is mass always compared to volume? Mass is just the quantity of matter, regardless of the volume. So shouldn't two objects of two different volumes still have the same weight regardless of their volume if their mass is the same or is mass always a function of volume?

That is what I have been taught but it could be wrong.

Edited by Uri
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I still don't get it. Why is mass always compared to volume? Mass is just the quantity of matter, regardless of the volume. So shouldn't two objects of two different volumes still have the same weight regardless of their volume if their mass is the same or is mass always a function of volume?

That is what I have been taught but it could be wrong.

Which has more weight, 10 kg of lead or 10 kg of feathers? What about if you weighed them on the moon?

Which has more mass, 10 lb of lead or 10 lb of feathers?

A lot depends on how you define your terms. Does a boat weigh nothing when floating in water - or just enough to displace an equal weight of water?

Edited by J.C.MacSwell
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So shouldn't two objects of two different volumes still have the same weight regardless of their volume if their mass is the same or is mass always a function of volume?

The answer depends on what you mean by "weight". Weight has multiple meanings.

• Legal weight. Legally (and colloquially), weight is a synonym for mass. A one pound can of beans weighs 10 pounds on the surface of the Earth, on the Moon, and on the space station.

• Gravitational weight: $W_g=m*g$, where m is the object's mass and g is the gravitational acceleration of the object. This is the definition of weight used in most introductory physics texts. One problem with this definition: It is unmeasurable.

• Scale weight: $W_s = \sum F_{\text{ext}}-W_g$, where Fext are the external forces (including gravity) acting on the object. This is the quantity measured by an ideal scale. This is the definition of weight used in some undergraduate physics texts very and is closely aligned with the definition of weight used in general relativity.

So, if you use gravitational weight as your definition, two objects with the same mass have the same weight. If you use scale weight as your definition, two objects with the same mass can have vastly different weights. One of the external forces acting on an object is buoyancy, and buoyancy is a function of the object's volume.

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Which has more weight, 10 kg of lead or 10 kg of feathers? What about if you weighed them on the moon?

Actually they should weigh the same in a similar gravitational field. Their mass should also be same. Unlike weight, mass is the amount of material an object contains and does not change under a different gravitational field.

A lot depends on how you define your terms. Does a boat weigh nothing when floating in water - or just enough to displace an equal weight of water?

If the boat is floating it's weight is equal to the weigth of the volume of water displaced.

Merged post follows:

Consecutive posts merged
Most would say less dense air is lighter generally, but it depends on what you are comparing and what you mean by lighter.

But why is less dense air lighter? By 'lighter' I mean has less weight or weights less and that is also the dictionary's definition of 'lighter'.

What I mean is that even if air expands in volume it's mass and hence it's weight should stay the same because mass is simply the quantity of material which a body contains, irrespective of its volume.

Edited by Uri
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Actually they should weigh the same in a similar gravitational field. Their mass should also be same. Unlike weight, mass is the amount of material an object contains and does not change under a different gravitational field.

If the boat is floating it's weight is equal to the weigth of the volume of water displaced.

Fair enough, you have used pretty much the same definition of weight in each case.

However, if you used a scale, 10 kg of lead would weigh more than 10 kg of feathers due to the greater buoyant force of the atmosphere on the feathers. That is more or less the definition some others have used in this thread. They have allowed buoyancy to be factored into the terms heavier or lighter. Still valid, but they are weighing things differently.

OTOH, mass is always defined the same way. So on the moon, with no buoyant forces from the atmosphere 10 kg of lead or feathers weigh the same, even on a scale.

The difference might be subtle, but become quite significant with respect to something as "light as air".

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Most would say less dense air is lighter generally, but it depends on what you are comparing and what you mean by lighter.

But why is less dense air less massive? This is what I don't understand.

By 'lighter' I mean has less weight or weights less and that is also the dictionary's definition of 'lighter'.

What I mean is that even if air expands in volume its mass and hence its weight should stay the same because mass is simply the quantity of material which a body contains, irrespective of its volume.

Edited by Uri
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By 'lighter' I mean has less weight or weights less and that is also the dictionary's definition of 'lighter'.

The problem here, Uri, is that you are stuck on the idea of weight being mass times gravitational acceleration. That is not the only definition. See post #9.

From http://www.thefreedictionary.com/weight (emphasis mine):

1. A measure of the heaviness of an object.

4. The measured heaviness of a specific object: a two-pound weight.

Note well: Gravitational weight cannot be measured. These definitions are alluding about some other aspect of the word "weight". They are in fact alluding to what I called in post #9 "scale weight".

Gravitational weight obviously is not the meaning of weight used in the article you cited in the original post.

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The word "lighter" has several meanings.

When comparing two masses, the lighter mass has less mass than the heavier mass. Eg, 1 kg of lead is lighter than 2 kg of styrofoam.

When comparing two substances, the lighter substance has a lower density than the heavier substance. Eg, styrofoam is lighter than lead, or your example, hot air is lighter than cold air.

As well, lighter can simply mean the weight is smaller. Eg, scuba gear is lighter when you are underwater (due to buoyancy), or you're lighter on the moon (due to lower gravity).

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What I mean is that even if air expands in volume its mass and hence its weight should stay the same because mass is simply the quantity of material which a body contains, irrespective of its volume.

The total mass of air has the same mass, yes. But any given volume of that air has less mass. That's what matters. It's like replacing 100 cubic meters of "heavy air" with 200 cubic meters of "light air." The light air gets forced upwards, to make room for heavier air. Yes, it contains all the same molecules. Yes, the total mass of each total volume is the same. But a cubic meter of light air is lighter than a cubic meter of heavy air, and that's what matters. That's all that's being said. Similarly, the whole weight of the Earth's atmosphere is a whole lot more than a cannonball, and yet you drop a cannonball and it falls right through the air, because, we say, it's "heavier than air." And by that we mean heavier than a mass of air occupying the same volume, i.e denser.

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But why is less dense air less massive? This is what I don't understand.

By 'lighter' I mean has less weight or weights less and that is also the dictionary's definition of 'lighter'.

What I mean is that even if air expands in volume its mass and hence its weight should stay the same because mass is simply the quantity of material which a body contains, irrespective of its volume.

This is a matter of definition. "Density" is the amount of mass per unit volume; for example, water (at standard temperature and pressure, "STP") has a density of 1 g per cm3. In contrast, gasoline has a density of around 0.75 g/cm3, and mercury has a density of 13.5 g/cm3. Gasoline is less dense than water; mercury is more dense. 100 mL of water will weigh 100 g, while 100 mL of gasoline will weigh about 75 g. It weighs less by definition.

The density of air at STP is about 0.0012 g/cm3. Air density varies with pressure (higher pressure raises density), temperature (density decreases with temperature), humidity (moist air is more dense than dry air), and composition (gases like CO2 increase the density).

This is the principle upon which hot air balloons rely. Hot air is less dense than cold air. So, if you heat the air inside your balloon, it becomes less dense. Since the pressure has to remain the same as the surrounding atmosphere (hot air balloons are not sealed), and the volume remains constant, raising the temperature means that the number of moles of gas included must decrease: PV = nRT, or n = PV/(RT). "R" is the gas constant, and does not change. Gas (air) leaves the balloon, so that the whole system is less massive -- therefore, the air in the balloon is less dense, and the whole thing rises.

Make sense?

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A few corrections.

This is a matter of definition. "Density" is the amount of mass per unit volume; for example, water (at standard temperature and pressure, "STP") has a density of 1 g per cm3.

Actually, that's what it is at 4 C, the temperature at which it is densest at standard pressure. However, it is usually very close to 1 g/cm3 at other temperatures.

humidity (moist air is more dense than dry air),

Actually, moist air is less dense than dry air (probably a typo on your part considering you know the ideal gas law). This is counterintuitive to people who note that liquid water is heavier than air. However, the molecular weight of water is 18 g/mol, compared to the heavier 28 g/mol for N2 and 32 g/mol for O2. Since the density of gases is related to the molecular weight of the gas, this makes moist air less dense than dry air.

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A few corrections.

Actually, that's what it is at 4 C, the temperature at which it is densest at standard pressure. However, it is usually very close to 1 g/cm3 at other temperatures.

Actually, moist air is less dense than dry air (probably a typo on your part considering you know the ideal gas law). This is counterintuitive to people who note that liquid water is heavier than air. However, the molecular weight of water is 18 g/mol, compared to the heavier 28 g/mol for N2 and 32 g/mol for O2. Since the density of gases is related to the molecular weight of the gas, this makes moist air less dense than dry air.

Moist air is heavier though, when it has liquid water suspended in the air. I think a lot of people consider that moist air.

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I stand corrected: humid air just feels twice as dense as dry air

I've been to Texas: I know

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Originally posted by GDG:

Since the pressure has to remain the same as the surrounding atmosphere (hot air balloons are not sealed), and the volume remains constant, raising the temperature means that the number of moles of gas included must decrease: PV = nRT, or n = PV/(RT). "R" is the gas constant, and does not change. Gas (air) leaves the balloon, so that the whole system is less massive -- therefore, the air in the balloon is less dense, and the whole thing rises.

Here, V must increase to keep P and n constant. n is the mole of the air inside the balloon, it cannot be changed as hot air doesn't leak out. With the constant n and larger V, its density is smaller, lighter.

Originally posted by Mr Skeptic:

However, the molecular weight of water is 18 g/mol, compared to the heavier 28 g/mol for N2 and 32 g/mol for O2. Since the density of gases is related to the molecular weight of the gas, this makes moist air less dense than dry air.

I doubt about this statement. What you talk about here is the molar mass, it is rather different with density. If we consider the moist as a mixture of water(liquid) and dry air, apparently, the density of moist air will be larger.

I can also explain in your point, 1 mole of dry air occupies much larger volume than 1 mole of water. The differences in volume is much larger than the difference in mass when we consider the same quantity of dry air and water. Overall result is that density will be increased when water droplet is added.

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Here, V must increase to keep P and n constant. n is the mole of the air inside the balloon, it cannot be changed as hot air doesn't leak out. With the constant n and larger V, its density is smaller, lighter.

I'm pretty sure GDG had it right for a hot air balloon. Your right that it doesn't or shouldn't leak out, but it certainly is free to get out, as it is open at the bottom.

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Overall result is that density will be increased when water droplet is added.

But you don't just "add" a water droplet. The water molecules in the air effectively "knock out" some of the other molecules in the air. If they didn't, the pressure would go up because there would be more molecules per unit volume, causing more impacts per unit area, resulting in higher pressure. But, we are assuming constant pressure and temperature when comparing the two.

And, since most of the molecules in air (oxygen and nitrogen being the overwhelming majority) are heavier than water, the water results in less overall mass per unit volume for a given pressure and temperature of humid air.

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I think that what he's saying is that air plus liquid water (eg mist or fog) is more dense then the air without that liquid water. That's true, but most people consider moist air to be air with lots of water vapor, in which case it will be less dense than dry air.

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Here, V must increase to keep P and n constant. n is the mole of the air inside the balloon, it cannot be changed as hot air doesn't leak out. With the constant n and larger V, its density is smaller, lighter.

Once the balloon is inflated, V does not increase. Hot air balloons do not work the same way as toy rubber balloons. The bottom of a hot air balloon is open: it has a burner suspended below the opening, which the operator (pilot?) flicks on every few minutes to heat the air inside the balloon. (Believe me, riding in a hot air balloon is a much noisier experience than you would expect. The burners are surprisingly noisy.) The balloon fabric does not stretch. Since P and V are constant, n must decrease with increasing T. Thus, hot air escapes from the bottom of the balloon, leaving a smaller mass of (hot) air inside the balloon.

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