How Does a Hot Air Balloon Produce Lift?

The less dense hot air weighs a certain amount. The more dense cold air that was replaced weighed a greater amount. The difference is the force that lifts the balloon. Sheesh.

You're correct on many key aspects but are not following through with the complete analysis. The pressure and densities of a hot air balloon are in the range that the ideal gas law applies.

PV=nRT

The bold symbols are the only values that will change. Since the number of moles (n) can be expressed by n=m/M with M being the average molar mass of the gas (air). Then a little simple algebra gives :

d^-1=V/m=(PM)^-1RT

So as the gas gets warm it gets less dense and rises.

Now if you have trouble understanding that anything in a fluid will rise if it is less dense than the fluid around it, just look at that ice cube in your drink.

Beginning with

d^-1=V/m=(PM)^-1RT

focusing on d^-1=V/m, given V is the basically fixed Volume of the balloon, then m the mass of the air atoms changed.

Buoyancy = variable molecular mass.

Being more realistic. What changes is V_m/m_n. The volume required for a single atomic mass. The molecular density. So, vacuum energy causes buoyancy?

However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?

"However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?"

I don't think that's true. All molecules are in motion within themselves having vibrational and rotational modes (plus of course the translational mode).There are 2 vibrational modes - "stretching" and "scissors." Both of these increase in amplitude with temperature. So an increasing amplitude stretching bond would effectively increase the average size of the molecule in the case of a diatomic molecule.

Is this relevant? Not sure.

"However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?"

All molecules are in motion within themselves having vibrational and rotational modes (plus of course the translational mode). There are 2 vibrational modes - "stretching" and "scissors." Both of these increase in amplitude with temperature.

YES

O2 and N2 are both linear diatomic so except for water vapor, scissors doesn't really apply. Amplitude does increase, but very very slightly. Mean bond length doesn't change.

The external kinetic energy per molecule does change. There is a documented change in the skew of the Boltzman curve with T.

The final question then is, how does heat accelerate ideal gas molecules?

The space between molecules changes, but I don't think the space changes between the atoms within each molecules. Even if it did, it wouldn't make much difference.

Here we have the confusion!

With a gas the volume of individual molecules and their bond length has nothing to do with the average volume occupied by each molecule. The molecules of a gas are free to travel through space and do travel that space for considerable distances (compared to the size of the molecule) before confronting another molecule. In a liquid the molecules are free to move but there space to move is limited because the molecules are effectively touching each other. This combination of attributes is pivotal for hydraulics to work. Then there are solids where the molecules are not free to travel and as such the molecules are effectively touching each other.

This relationship of the number of molecules a gas will contain in a volume of space is how the molecular mass of aromatic compounds are measured. An arbitrary volume of the liquid is poured into a flask with a known total volume. The flask has a small opening to atmosphere (usually foil with a slit) and a thermometer inside the flask. The flask is slowly heated until all of the fluid vaporizes. At the moment of complete vaporization the temperature of the gas is recorded. The flask is now quickly chilled (ice bath commonly) so that the known volume of vapour condenses back to a liquid. The mass of the liquid is found by weight. A little simple mathematics follows and bingo. The average molar mass of the remaining liquid has been found.

Air expands as it is heated.
Hot air has the same mass as it had when it was cold, but it now occupies a larger volume as it has expanded. Thus it is less dense thus it rises.
Next!
Del

Wow. You're way ahead of me. I'm still trying to figure out why the balloon floats on water and doesn't sink?

There are times when ignorance is bliss. This is one for me.

I'm not sure why one would insist that everything must have a mathematical explanation.

How do you model the behaviour of a helium filled balloon in a closed car?

Why is there no light diffusion in a vacuum, mathematically?

Are we there yet?

The energy source for the lift is gravitational potential energy, not heat (or only indirectly heat).

If things can move, the heaviest stuff goes to the bottom, as this minimizes the total gravitational potential energy of the system. (Same reason that water flows down.) The decrease of overall energy provides the lifting energy for the lighter stuff.

Is this, " gravitational potential energy" what keeps boats afloat, too?

Gravitational Potential Energy

Yes.

Dare I suggest this is all "much ado about very little?"

I agree. Let's "float" the idea and see where it goes.

I'm good...

If people don't know how air works, can we call them airheads?

ξ

Medically speaking they would be pneumocephalads, and (in order to NOT be off topic), since the cranial bones cannot expand to allow enough cold air to be displaced by the expanded heated air to 'offset' the weight of the patient, they will never get airborne.

The hot air has less mass per unit volume than the outside colder air. The balloon floats up, exchanging places with the colder air above, converting gravitational potential energy into kinetic energy.

Hot air up the middle cooler air out down the side thus the hot air occupies has the same voulume but is much less dense. There is your lift.

OK, all the above is but an oversimplified model of yours, because obviously some of the air is replaced by a mixture of CO2 + H20 from burned propane, some of the water vapor will condense and drop, and some will diffuse thru the envelope, and CO2 is denser than air but will be partially absorbed by algae on the inner surface (depending on envelope color, of course), and...

I suspect one can learn much about hot air balloon physics by turning the balloon upside down and noting differences in operation.

Nah...solar balloons retain their mass and are non-expandable (to a point) working solely on the principle of hot air rising.

There is no loss of the heated air mass...

I think we are nuking this

The solar balloon is not initially fully inflated. That allows the air mass to expand thus changing its displacement.

Yeah, but none of this nonsense:

"...thus reducing the mass by expelling a portion of the heated air mass."

whatever...

You've blown your credibility, already. Why not quit while you're ahead.

The damn thing floats because the volume of air that the balloon displaces is LIGHTER than the volume of air that the balloon displaces.

The hot air around here seems to be escaping from you!

"The damn thing floats because the volume of air that the balloon displaces is LIGHTER than the volume of air that the balloon displaces."

Well, DUH. In the solar balloon, the initial air mass is signifigantly smaller than the fully inflated size of the balloon. As it heats up and expands, it displaces a larger volume of air - its mass never changes only its volume.

HOWEVER - in a conventional hot air balloon *once its fully inflated* the trapped air mass can and DOES change its total mass as the opening in the bottom allows a portion of the air mass to escape as further heating causes the pressure to rise. This reduction in the total air mass (by further heating) is what allows the balloon to rise further after it has reached equilibrium. THAT is what I was referring to in my original post.

What makes the difference is that the baloon is open on the bottom and allows air voulume to escape and leave a less dense hot air in the baloon creating the lift.

If the ballon can not expand and is closed and you heat it up nothing will happen.

Cheers IS

Well, it may explode.

This thread has exploded already.

You say it! All hot air!

How could I've overlooked this for so long. You're the wizard and you still don't know how it works.

After all of the mish-mash mumbo-jumbo and math...

Next thing you know someone will say that bumble-bees can't fly because the math doesn't work...yeah, okay

yikes.

Heat rises. The balloon traps the hot air. A pocket of hot air surrounded by cold air will rise.