Why is hot air lighter than cold air?

Is it less dense? Does the mass of the moving molecules convert into the energy of heat? What about solids? Is a hot frying pan lighter than a cold frying pan?

 

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Yes, that's generally what "less dense" in this context means. It is related by PV=nRT. So if temperature goes up (for example), and nothing else but volume can change, volume goes up and therefore density goes down.

No. The mass stays the same, the volume increases.

It will expand and become slightly less dense, but generally people think of "light" and "heavy" for solid objects in terms of weight. The weight stays the same (except for relativistic effects, which are negligible).

 

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How does the volume of air increase but its weight decrease? Isn't the mass of that expanded parcel of air the same? Also why is density a factor? If I take a piece of bread and roll it into a ball of dough, its density has increased. But it doesn't mean it's heavier now does it?

 

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Its weight does not decrease, just its density. Mass stays the same, volume increases, so density decreases.

Correct.

Sorry, there was a wording error in my first post. That first sentence should have said: "Yes, that's generally what "lighter" in this context means."

You asked: "why is hot air lighter... is it less dense?" The answer is a simple yes.

 

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So hot air isn't really lighter than cold air? IOW, it's mass is the same?

I don't understand how a change of density in matter but not its mass changes its weight. Let's take water for example. Will hot water be lighter than the same amount of cold water just because we changed its density?

 

It's mass is the same, but when people say "lighter" in some contexts they are referring to density. "Lighter" isn't really a scientific term.

A change in density, but not mass, does not change its weight. Only its volume.
D=M/V
If volume changes, density changes even if mass stays the same.

Hot water will be slightly less dense than cold water. Again, "lighter" is not really a scientific term, so it depends on what you mean by it.

You may also be confusing this all with buoyancy...

 

By lighter or heavier I mean the amount of the pull of gravity on the atoms of that quantity of matter. Gravity is obviously pulling on the air when it is both hot and cold. Does that pull change for those atoms or not?

Let's try this experiment. Place a balloon filled with cold air in a vacuum. Now heat the air in the balloon. Will the pull of gravity on the balloon now be less or the same?

 

The statement "hot air is lighter than cold air" includes the tacit condition that it talking about equal volumes of air. It means that hot air is lighter than an equal volume of cold air. Thus if you have two balloons of equal size, the one filled with hot air will be lighter than the one filled with cold air. No one is stating or implying that heating a given quantity of air will make that quantity of air weigh less.

 

The assumption seems to be that increasing a volume of air will make it weigh less. Why? It's the same amount of atoms in both cases. The only thing that is added is space, which weighs nothing.

 

I agree with Russ that the confusion here seems to be because your balloon thought experiment introduces bouyancy.

Your hot air balloon rises because it is bouyant. It is bouyant because the volume it occupies weighs less than the equivalent volume of the air surrounding it. This is also why ships float. The explanation is Archimedes' Principle, explained at length here: https://en.wikipedia.org/wiki/Archimedes'_principle

As others have pointed out, when we say heated air becomes "lighter" we speak a bit loosely. In the context of a hot air balloon the volume is fixed. (The envelope does not stretch, because it is open at the bottom.) Consequently, as the air is heated it expands, pushing air out at the bottom. So the total mass of air in the envelope reduces, the hotter it gets. So the total mass of the balloon does indeed become less and eventually a point is reached at which the total mass is less than volume of surrounding air it displaces, and then, due to Archimedes' Principle, it floats up. If you have a hot air balloon in a vacuum, you get no lift from it, because there is no denser medium surrounding it which it is displacing from the volume it occupies (just as a ship will not float in air).

If you have a closed rubber balloon, on the other hand, and you heat the air inside, the mass cannot change but the envelope stretches as the pressure inside rises, so this time it is the volume that increases rather than the mass decreasing. But the effect is the same: eventually the volume occupied weighs less than the equivalent volume of the surrounding air and, by Archimedes' Principle, you get lift.

Hot air, for example heated by contact with hot ground on a sunny day,will rise, because it has become less dense (has less weight for the volume it occupies) than the cooler air above it.

The reason air expands as it is heated is that the molecules have more thermal kinetic energy, move faster and rebound off each other harder, thus causing the mean distance between them to increase. The same mass thus occupies a greater volume, i.e. its density has gone down. If you prevent this expansion by putting it in a closed vessel what happens is the molecules rebound harder off the sides of the vessel, resulting in an increase in pressure instead, while the density remains unchanged.

Mathematically, Pressure x Volume is proportional to Temperature.
PV = nRT (where n is the number of molecules and R is a constant called the Gas Constant.) This is known as the perfect gas equation - or ideal gas law - and is foundational for a lot of physics, engineering and chemistry.

 

Several have told the PV = nRT describtive relationship but no one has tried to directy answer the question, tell the physical mechanism, so I will:

When a gas molecule strikes a confining wall it either briefly sticks or rebounds. In either case force is applied to the molecule by the wall as its momentum has either been zeroed or reversed. On the average "hotter" gas molecules have greater momentum than cold ones do so the average force on a square cm of the wall, say a rubber balloon, containing the hotter gas will be greater than when the gas is colder.

We call this average force /cm^2 "pressure." Thus a given number of "hot molecules" inside a balloon will make the balloon radius larger than the same number of colder molecules will as their presure is greater. The same number of molecules in that larger volume will have a lower density - I. e. the hotter gas has lower density and is "lighter."

 

That's weight. No, it doesn't change.

It will be the same.

 

That isn't quite the correct mechanism. A balloon has roughly the same pressure up to a maximum volume (dependent only on its elasticity: if you use a mylar bag, it has no significant elasticity). Since the momentum of the collisions increases and the pressure has to be balanced, the bag expands to reduce the number of collisions per unit area and thus keep the pressure constant.

 

No. That is exactly the mechanism. I did not postulate any relationship between balloon volume and internal pressure as that was not needed, but in general, up until it bursts, the balloon does expand with increasing internal pressure (assuming the external air pressure is constant) and that is stretching the balloon skin ever more until failure.

I.e. it is false that: "A balloon has roughly the same pressure up to a maximum volume" for the typical rubber balloon.

 

It's about displacement. The hot air inside a balloon displaces an equal volume of cooler air outside the balloon. The hot air is less dense, so yes, it has fewer molecules than the cooler air that it displaces and therefore the pull of gravity will be less. Of course, in a vacuum there is no displacement so the balloon can not "float".

 

I think the idea of buoyancy or displacement answers my questions pretty well. I picture the heated air being sort of pushed up by the denser cold air rushing in underneath it. Like how a bubble rises quickly in an aquarium. The denser medium "squeezes" the hot air up like a tube of toothpaste. The question of why it does this from underneath and not on all sides of the parcel of hot air remains open however. IOW, why isn't the medium of denser air exerting an equal pressure of displacement on all sides of the hot more vaccuous air, effectively causing it to be stationary?

 

That is a different question than "Why is it lighter" (Which I expained in post 13.) and easy to answer:
The total pressure on the top half of a sherical bubble or balloon pushing down is less than than the total pressure on the bottom hemisphere pushing up.

The presure difference between top and bottom halfs, increases with bubble diameter - why big bubbles rise faster than smaller ones do (but there are a few other minor factors to consider if you want to get quantative - mainly the inertia of the mass above that needs to be pushed out of the way). This pressure force difference is of course much greater if the rise is thru water than if thru air, but principles are the same.