Does Gravity Cause Hotter Water at the Top of a Tower?

[rockandroll]

Hello, I have an interesting question about water natural convection without an external heat source.

Say we have a high tower filled with water. The tower walls don’t allow any heat to escape or enter the system. There is a constant gravitational force present in a system (g-force). At the beginning the water is all at the same temperature.

The water naturally contains faster and hotter atoms and slower and cooler atoms. Because of the buoyancy forces the hotter atoms will have a tendency to rise and cooler atoms will have a tendency to sink.

Is it correct to say that after some time the water at the top of a tower will become hotter than the water at the bottom of a tower? Or the heat transfer will cancel out this effect?

 

[mfb]

Because of the buoyancy forces the hotter atoms will have a tendency to rise and cooler atoms will have a tendency to sink.

That is true for regions of hot water, but not for individual particles. There are no "hot atoms", just atoms with a high energy.

 

[rockandroll]

That is true for regions of hot water, but not for individual particles. There are no "hot atoms", just atoms with a high energy.

You are right.
But, since atoms move through the liquid relatively freely, small regions of hot and cold water will randomly appear in the water.

Hotter regions will rise and cooler regions will sink.

This doesn’t change the question .

 

[K^2]

If that was the case, there would be a temperature gradient. I could attach a Sterling engine and get free energy. So clearly, what you suggest is a violation of laws of Thermodynamics. A more interesting question is why.

Well, first of all, you need to realize that in order for fluid to change density with temperature, it must be compressible. Suppose, you ended up with a small pocket of slightly warmer fluid due to random fluctuation. It will begin to rise, yes. But as it rises, it will experience a pressure change and will expand. That expansion will do work against the fluid surrounding it. That will cool the pocket of fluid in question and will heat up the rest of the fluid. So the system will tend towards equilibrium.

In order to have convective flows, one must have a non-equilibrium situation to begin with. Most typically, in the form of a heat source or a temperature gradient.

All of this plays a huge role in atmospheric science and weather. Because we do have uneven heating on the planet, you do end up with convection flows. These act as planet-scale heat pumps. That sets up regions of stable and unstable air. That dampens convection in some places and causes runaway convection in others. But the power source for all of this is the Sun. If there was no Sun, and instead, we had an even temperature background in all directions, the atmosphere would be exactly the same temperature at every altitude.

 

[94JZA80]

All of this plays a huge role in atmospheric science and weather. Because we do have uneven heating on the planet, you do end up with convection flows. These act as planet-scale heat pumps. That sets up regions of stable and unstable air. That dampens convection in some places and causes runaway convection in others. But the power source for all of this is the Sun. If there was no Sun, and instead, we had an even temperature background in all directions, the atmosphere would be exactly the same temperature at every altitude.

i'm not so sure this is correct. even if there were no sun to heat our planet and there existed an even temperature background in all directions, the Earth's own gravity would still result in a pressure gradient in the atmosphere. with more weight bearing down on the air near the Earth's surface than the air at higher altitudes, we get a pressure gradient (its common knowledge that atmospheric pressure is greater at lower altitudes than at higher altitudes, other factors being equal). that pressure gradient will cause air under higher pressure to rise in temperature, resulting in a temperature gradient. now that a temperature gradient exists in the atmosphere, convection must take place, regardless of the existence of an external heat source (the sun).

In order to have convective flows, one must have an equilibrium situation to begin with. Most typically, in the form of a heat source or a temperature gradient.

did you mean to say non-equilibrium initial conditions? if things are initially in equilibrium, and there exists no heat source to change that, then we can't have a gradient - temperature, pressure, or otherwise. and without a gradient, nothing is going to convect, right?

 

[mfb]

You are right.
But, since atoms move through the liquid relatively freely, small regions of hot and cold water will randomly appear in the water.

I would expect that those are so small that they do not matter. Movement of small regions is randomly as well.

even if there were no sun to heat our planet and there existed an even temperature background in all directions, the Earth's own gravity would still result in a pressure gradient in the atmosphere.

Pressure gradient: Sure
Convection: Yes, as the atmosphere would not be in equilibrium - the ground is warmer than space. If the ground would have the same temperature as space (and ignoring that this is below the boiling point of air), we would not have convection, and get a uniform temperature everywhere.

 

[K^2]

i'm not so sure this is correct. even if there were no sun to heat our planet and there existed an even temperature background in all directions, the Earth's own gravity would still result in a pressure gradient in the atmosphere. with more weight bearing down on the air near the Earth's surface than the air at higher altitudes, we get a pressure gradient (its common knowledge that atmospheric pressure is greater at lower altitudes than at higher altitudes, other factors being equal). that pressure gradient will cause air under higher pressure to rise in temperature, resulting in a temperature gradient. now that a temperature gradient exists in the atmosphere, convection must take place, regardless of the existence of an external heat source (the sun).

If ground and cosmic background are at the same temperature, the atmosphere will have same temperature throughout. Again, the simplest proof is that if this wasn't the case, you could build a machine that generates free energy.

As far as why your argument doesn't hold, in order for air to heat up as it goes down or cool as it goes up, there must be actual convective flows. But if you try to push a small quantity of air down, it heats up, and becomes more buoyant. Without input of energy, the atmosphere tends to stabilize. Without flows, there is no compression or expansion, and therefore, no heating or cooling.

On the actual Earth, the planet, we have convective flows due to Earth being heated unevenly that do exactly what you describe, giving us warmer air at ground level and colder air higher up. (Then the temperature starts to rise, of course, but that has to do with solar radiation, etc. Completely beside the point.) Also, note that if you happen to have heavy cloud layer, the equilibrium temperature ends up at altitude, with surface being heated by this process. This is actually the main mechanism responsible for surface temperature of Venus and a contributing factor for temperature of Earth. (The standard "greenhouse" explanation is incomplete, and covers only a fraction of radiation spectrum.)

did you mean to say non-equilibrium initial conditions?

Yes, of course. I've mistyped.

 

[rockandroll]

Thanks for all your answers, folks.

 

[94JZA80]

but you said yourself:

In order to have convective flows, one must have a non-equilibrium situation to begin with. Most typically, in the form of a heat source or a temperature gradient.

...can't gravity alone provide that convection? can't gravity alone (in the absence of both solar and thermal energy sources) provide that source of energy and temperature gradient? as cooler, denser air settles at low altitudes, and as warmer, less dense air rises to high altitudes, a density/pressure gradient develops in the atmosphere. once the magnitude of the gradient is sufficient, the weight of the upper atmosphere compresses, and therefore heats, the lower atmosphere, causing it to rise and expand, while the upper atmosphere, which was initially warmer and less dense, is now cooler and denser than the rising and expanding lower atmosphere, and falls to the bottom to take its place, where it in turn gets compressed again. isn't that more or less convection?

 

[mfb]

...can't gravity alone provide that convection?

No. This can be seen with the second law of thermodynamics.

as cooler, denser air settles at low altitudes, and as warmer, less dense air rises to high altitudes

You have to decide what you want: Cooler upper atmosphere? Then you cannot get a cooler lower atmosphere at the same time and place.
While it might be possible to have some initial oscillation based on the initial conditions, this is damped and will die out after a while.

 

[94JZA80]

ok, thank you for the additional clarification...i think now that I'm starting to understand, but i definitely don't have a complete grasp on things yet.

i understand that entropy always increases in an isolated system via the 2nd law, but I'm failing to see why gravity alone cannot provide the energy needed to eventually induce atmospheric convection. i suppose it would be better to ask at what point does the process i described fail? does gravity not create a pressure gradient in the atmosphere? is air at higher atmospheric pressure not more dense (from being compressed by the weight of the air above it) than air at lower atmospheric pressure? would that process not impart energy to and heat the air being compressed, causing it to rise and expand?

 

[K^2]

The pressure gradient exists, of course. In fact, if temperature was constant throughout the atmosphere, and we could assume constant average mass of the molecules (it's not far off) it would be very easy to show that P(h) = P(0)*exp(-k h), where h is altitude and k is a constant you can derive from composition of air and ideal gas law.

But pressure gradient by itself isn't enough to set up a convective flow. You must have heat flow as well.

 

[mfb]

Gravity is a conservative force - you can extract it once, but not infinitely. If your mechanism lowers the center of mass of the atmosphere, there is no way to go back to the initial conditions (again, neglecting initial oscillations).

 

[boneh3ad]

I'd like to throw in that water is "compressible enough" to have heat-based convection. Water is typically considered incompressible, but it isn't truly and completely incompressible. Its compressibility is simply so low that compressibility effects can be safely neglected.

A good example of this is the appearance of Rayleigh-Bénard convection cells in water. Take, for example, the old fashioned hot chocolate that was more of a chocolate bar that you would heat up in a pot with water. When the chocolate is mixed in, you can see the convection cells develop. A really neat video of it is here:

 

[K^2]

Yes, I actually mentioned that requirement in the opening of my first post here. But with gasses, all of this is much more intuitive, so it's usually easier to explain how it works in a gas, and then point out the necessary conditions in the fluid.

 

[sophiecentaur]

. .. . . I'm failing to see why gravity alone cannot provide the energy needed to eventually induce atmospheric convection. i suppose it would be better to ask at what point does the process i described fail? does gravity not create a pressure gradient in the atmosphere?

As stated earlier, gravity is a conservative force - it is not a source of energy any more than a spring. You wouldn't dream of suggesting that you could get a continuous supply of energy out of a spring. All you would get would the what had been put in by winding it initially (Potential Energy).
Any other 'sneaky' arguments which try to get round this basic fact will just have to be ignoring something about the energy situation. Don't be misled into trying to design a perpetual motion engine.

 

[K^2]

It's sometimes useful to try and design a perpetual motion machine. If you think, "This ought to work," and that results in net energy production, then you are making a mistake somewhere. It's a useful diagnostic tool, because it tells you with absolute certainty that there is an error in some of your assumptions, which makes it easier to find these errors.

This is kind of the case here. We can use perpetual motion argument to state right away that proposal won't work, but that's not a sufficient explanation in its own right. There is still some conceptual error that lead OP to this fault, and it's more useful to try and find what that is. Which this thread has been all about, actually.

 

[94JZA80]

thank you for the extra clarification guys. i didn't realize at first that i was essentially portraying gravity as a perpetual motion mechanism in this context. things are starting to make sense now...