Can Altitude Hypothesis Challenge the Second Law of Thermodynamics?

[D H]

The pressure gradient that striphe is talking about results from hydrostatic equilibrium. The temperature gradient results from static conditions given hydrostatic equilibrium. In other words, nothing is flowing. So, no, this particular gradient cannot be mimicked in the way you are thinking.

 

[RonL]

The pressure gradient that striphe is talking about results from hydrostatic equilibrium. The temperature gradient results from static conditions given hydrostatic equilibrium. In other words, nothing is flowing. So, no, this particular gradient cannot be mimicked in the way you are thinking.

I will admit I was thinking flow, but when I said "a pressure gradient set between them" I was also thinking of a possible lock with check valves, so if this will not work, I can take it that the length of the tube is as important as the pressure gradient ?

Ron

 

[D H]

It is the length (actually, the height) of the tube that enables the pressure gradient to occur. The pressure at some point x in the tube is equal to the weight of all the gas in the tube above the point x divided by the cross sectional area of the tube.

 

[striphe]

in this static and closed system, will a heat gradient exists?

 

[striphe]

D H, i am unsure of your position concerning if a heat gradient will exist in a very tall body of gas in a closed system.

 

[D H]

The temperature gradient is simple physics. It results from a static gas subject to hydrostatic equilibrium, heating primarily from below, and adiabatic conditions.

Whether this is a viable energy source is a different question. The answer to that question is most likely no.

 

[stewartcs]

...The pressure at some point x in the tube is equal to the weight of all the gas in the tube above the point x divided by the cross sectional area of the tube.

Just to clarify...in general this is not true. The pressure is not dependant on the cross-sectional area of the tube (remember Pascal's Paradox). Hydrostatic pressure is equal to pgh (density x gravitational acceleration x fluid height).

CS

 

[D H]

The pressure is not dependant on the cross-sectional area of the tube (remember Pascal's Paradox).

I was trying to keep it simple, Stewart. The (maybe too implicit) assumption was one of a cylindrical tube.

Hydrostatic pressure is equal to pgh (density x gravitational acceleration x fluid height).

That is only true if density and gravitational acceleration are constant. A more generic form, and this is the form used in the development of the standard atmosphere models, is

$$\frac{\partial P}{\partial z} = -\rho g$$

This expression applies to the interior of the Earth, the interior of stars -- and the Earth's lower atmosphere.

 

[striphe]

There is no way that I would consider that building something similar to these thought experiments is a viable alternative source of energy. The issue is that if even theoretically one could achieve some kind of surplus energy, even if minuscule it looks likely to defy the second law of thermodynamics. Looking around the web there is no explanation of how a temperature gradient formed by gravity is compatible with the second law of thermodynamics.

D H, your expertise seems to be in fluid mechanics, which pays significant attention to the effects of gravity on a gas. In thermodynamics the focus isn’t on the effects of gravity on large bodies of gas and the generalisation is made that over time a body of gas will assume the same temperature and pressure at any location. You have asserted part A of the hypothesis as being correct, but it seems you are unable to explain why part B is wrong.

The people who read this and have an expertise in thermodynamics seemed to have dropped out of discussion and are allowing this unexplained compatibility of the tall body of gas heat gradient and the second law of thermodynamics to continue to be unexplained.

 

[D H]

The issue is that if even theoretically one could achieve some kind of surplus energy, even if minuscule it looks likely to defy the second law of thermodynamics. Looking around the web there is no explanation of how a temperature gradient formed by gravity is compatible with the second law of thermodynamics.

What makes you think that the second law of thermodynamics, at least naive versions of it such as those commonly found on the internet even applies here? The Earth (and its atmosphere) is not an isolated system. The Sun is pouring about 1.740×10¹⁷ watts (174 petawatts) of energy into the Earth.

 

[striphe]

I am aware that the Earth is not an isolated system. The earth’s atmosphere is used in thought experiment one, because when people think a long tube of gas, they make the possible generalisation that it has the same temperature and pressure at any location with the tube. Highlighting the often experienced fact that it colder at higher altitude, i wanted to highlight the effect gravity has on the temperature of the atmosphere.

When I raise the issue, I convert over to in isolated system as I considered that now readers would not make the generalisation and also consider the effects of gravity on this isolated system. There exist many versions of the law, but I would consider that the Clausius statement, the one that is most easily recognisable as being relevant.

"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature"

Consider a very long tube of gas that is isolated, that is affected by a massive gravity field. If on introduces heat energy to it, conduction will disperse the energy throughout. To add heat energy at any location will result in every location having an increased temperature.

If a heat gradient exists in this closed system due to gravity, then introducing heat energy to the colder top would result in heat energy moving from a colder material to a hotter material. This would defy the Clausius statement.

 

[D H]

"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature"

That is precisely what I meant by "naive versions of it [the 2nd law of thermodynamics] such as those commonly found on the internet." Where is entropy in that statement? Where the math?

When you do the math, assuming an ideal gas and maximizing entropy, you will get a gas that is under hydrostatic equilibrium and has a constant lapse rate. That entropy is maximized is built into the derivation of the adiabatic lapse rate. Entropy is evenly distributed throughout the vertical column. Pressure, density, and temperature are not.

 

[striphe]

So you are confirming that:
(a) If heat energy is added at any location in a body of gas will be distributed throughout the body.
(b) a heat gradient can be formed by gravity in a static body of gas

Have you, based on the above, concluded that the Clausius statement is a generalisation that doesn't apply in all situations?

 

[D H]

The Clausius statement does not apply here. A system that is subject to an external force such as gravitation cannot be an isolated system. Think about it for a second.

Edit
The Clausius statement does apply here. Gravitation is the source of energy that powers this system.

 

[striphe]

So you can harness gravity as a source of energy? This is new to me, can you explain how that works

 

[D H]

People have been building dams for a long, long time to harness gravity as a source of energy.

 

[striphe]

Ok, it looks like i misunderstood what you meant by gravity as a source of energy.

Could you go into a little more detail so that we are on the same page.

 

[striphe]

In terms of the situation in question

 

[RonL]

Ok, it looks like i misunderstood what you meant by gravity as a source of energy.

Could you go into a little more detail so that we are on the same page.

Let me throw out something that might give you a possible option for thought.

Couldn't find what I wanted (a good indicator of ones age) I'll keep looking.

Try to find an illustration of an old coffee percolator pot that had the internal mechanics that lifted the weight of the perking unit and grounds container. The pumping action came from heat transfer and pressure buildup, the lifted weight and gravity return, produced a continual cycle as long as heat was applied to the heat element.

I think this might qualify as an example of what is being discussed.

Ron

 

[striphe]

The old coffee percolator pumping action is powered by an internal heat engine from the sounds of it.

the energy transfer would be, electrical -> heat -> kinetic -> gravitational potential

That gravitational potential could then be converted to utilisable forms.

The coffee percolator is different from these hypothetical gas tubes.

The way that they would harness energy if physically able to is based on the formation of heat gradients. Its not gravity that would power such a devise, but heat energy.

Gravity is very important as it induces this heat gradient in a gas. The reason that gravity does not power these devises, is based around the idea that every down movement is countered by an equal up movement. When you have a dam, to extract energy from the dam, you have to have the water move from a higher postion to a lower postion.

Any system that converts net gravitational potential energy into some other form, will always incur that the systems centre of mass moves from a higher position to a lower position. Consider if this would occur with the hypothetical devises.

My difficulty with D H's proposal of what actually powers these hypothetical devises comes from the above static centre of gravity consideration.

I think that the focus should shift for a moment from how these devises arn't perpetual to the background science behind the heat gradient and how this heat gradient can co-exist with the Clausius statement.

 

[D H]

Striphe: That the gas has a pressure gradient is a simple application of the Navier-Stokes equation. Another way to look at it: The gas will minimize the Lagrangian at all points throughout the tube. That the gas has a temperature gradient is a simple application of reversible adiabatic (i.e., isentropic) conditions. Another way to look at it: The gas will maximize the total entropy.

 

[striphe]

Anyone want to explain how the tube of gas doesn't violate the clasius statement?

 

[D H]

Clausius statement, "Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature", is just words. The statement has two weasel words in it to boot: "generally" and "spontaneously". It is much better to look at the math. The temperature gradient exists precisely because of the second law of thermodynamics. You can find the mathematics behind the adiabatic lapse rate at many sites on the 'net.

How is the temperature gradient consistent with kinetic theory? Consider a small packet of air molecules at some temperature T and some height z in the tube. Those air molecules are moving about, colliding with the walls of the tube and with other molecules. The average kinetic energy of those molecules is, assuming an ideal gas, purely a function of the temperature T. Some of the molecules will be moving upwards, others downwards.

Let's look at the molecules whose velocity vectors have an upward component. The molecules will move upwards some distance before striking another molecule or a wall of the tube. In that time, gravity will have slowed the upward-moving molecules down a bit: Gravitation has in a sense reduced the temperature of the upward-moving molecules prior to the collision. The opposite happens to the downward-moving molecules: Gravitation increases their temperature.

In short, the temperature gradient is consistent with kinetic theory.

 

[stewartcs]

People have been building dams for a long, long time to harness gravity as a source of energy.

Are you implying that gravity is an energy source?

CS

 

[D H]

What do you think powers hydroelectric generators? The immediate source of energy power is the kinetic energy in the flowing water. That kinetic energy results from the gravitational potential energy difference between the top of the dam and the bottom of the turbine.

 

[RonL]

What do you think powers hydroelectric generators? The immediate source of energy power is the kinetic energy in the flowing water. That kinetic energy results from the gravitational potential energy difference between the top of the dam and the bottom of the turbine.

Is the Earth's rain cycle considered a perpetual event ?? I would think it is.

 

[D H]

Is the Earth's rain cycle considered a perpetual event ?? I would think it is.

Nothing lasts forever. The Sun will burn itself out eventually, and the Earth (if it exists) will cool to the background radiation temperature. Before that, the Sun will pass through a red giant phase that may engulf the Earth. Before that, the Sun's ever increasing output will result in the oceans evaporating away. Plate tectonics may stop before that, so even before the oceans disappear the Earth will be a flat, barren landscape.

All of this is terribly off-topic. So let's get back on topic.

 

[stewartcs]

What do you think powers hydroelectric generators?

Uh...falling water?

The immediate source of energy power is the kinetic energy in the flowing water.

I agree...other than I don't know what "energy power" means together.

That kinetic energy results from the gravitational potential energy difference between the top of the dam and the bottom of the turbine.

Also true.

...

However, the potential energy stored in a particle of water didn't come from gravity, it came from the work done on it to get it to the top of the dam. Something must have expended energy to put the water particle at the top of the dam, that something wasn't gravity.

Gravity certainly plays a role in potential energy by providing a force field but I don't agree with the statement that it is a source of energy.

CS

 

[D H]

However, the potential energy stored in a particle of water didn't come from gravity, it came from the work done on it to get it to the top of the dam. Something must have expended energy to put the water particle at the top of the dam, that something wasn't gravity.

That is akin to arguing that petroleum products and coal are not sources of energy because something else expended energy to convert biological wastes into oil and coal.

That said, this discussion is veering far off-topic. Please stick to the topic at hand, which is the pressure and temperature gradient in the Earth's atmosphere.

 

[RonL]

Nothing lasts forever. The Sun will burn itself out eventually, and the Earth (if it exists) will cool to the background radiation temperature. Before that, the Sun will pass through a red giant phase that may engulf the Earth. Before that, the Sun's ever increasing output will result in the oceans evaporating away. Plate tectonics may stop before that, so even before the oceans disappear the Earth will be a flat, barren landscape.

All of this is terribly off-topic. So let's get back on topic.

There has been close to a dozen topics covered so far in this thread, the copper wire with perfect insulation, except for a little exposure at top and bottom was one, I think it might be quite warm at top, in the cold area.
My connection about the coffee pot, a rain cycle and your comment about the water behind a dam, goes to the changes of a liquid to gas, using heat of the Earth's surface and the cold air at high altitude.

If located in a hot region (a desert) and using a tank of say propane, holding some volume of liquid, how tall would a closed pipe need to be in order for it to reach a point of gas vapor condensing back to liquid and fall like rain and be collected in a vertical height and weight producing value ? There would need to be an inside pipe (insulated) open bottom and top that would carry the gas vapor to a very high and cold altitude within the outer closed pipe.

Heat is provided by the hot air at ground surface, propane boils, check valves between the inside and outside pipe force gas to flow upward through the inside pipe to as high as needed to reach a point of condensation, based on pressure and temperature, so that it rains back down between the two pipes.
Taking energy out of the system can be many different ways.
The question will be how tall will this have to be ?
In post #1 shifting of large water tanks was mentioned, so the discussion has to be mechanical, heat engines are mentioned, so thermal transfer is in play.

Ron

 

[striphe]

It's good to see some commenting going on in this forum; it has been very slow for a long time.

The mention of copper by me was an attempted preface to thought experiment 2, which relies on heat gradients that are formed by gravity differing from material to material.
You have to remember that collisions are not the only way that heat energy dissipates throughout the gas. Each particle emits electromagnetic radiation which also transfers heat to the other particles.

It is interesting to consider if a heat gradient from by gravity alone will allow a perpetual cycle of vaporisation and precipitation to occur. I would have doubts in such, as the temperature and pressure differences are related and I would expect that as the temperature drops closer to condensation point at a lower altitude, the pressure is lower and the condensation point is higher than at the lower altitude. I assume that this would disallow such perpetuation, but it doesn’t mean it could not be induced to the advantage of being utilised for energy. I might go further with this if requested, but the two experiments proposed are simpler and should be explored first.

The Clausius statement and the entire second law of thermodynamics is a generalisation as it does not apply to very small systems; it is more or less enforced in large systems due to the law of large numbers. The clauses inherent in the statement refer to these small systems and not large systems such as the ones that are being discussed.

If we are going to look at math, let’s look at the math of experiment two. What we need is two tubes of material (solid, liquid or gas) that are the same length, affected by the same gravity field and have the same temperature at the bottom. The variables for each should be chosen so that for one tube, the least possible gradient emerges and the other should have variables chosen that result in the most possible heat gradient. Can this be done ?

 

[D H]

The "simultaneously" clause in Clausius statement most certainly does pertain to large systems. It is quite possible to transfer heat from a colder object to a warmer one. You probably have at least two such devices in your house that do just that. The trick is that work is required.

Striphe, before making any more Rube Goldberg thought experiments it would be best to get back to basics. You have been having difficulties even understanding the basics. The goldberg-esque thought experiments are not helping.

 

[striphe]

"Heat generally cannot flow 'spontaneously' from a material at lower temperature to a material at higher temperature."

Change clauses to clause, as I was referring to the "generally" clause. I'm not sure where this "simultaneity" clause comes from.

I don’t want to complicate things with more thought experiments.

 

[D H]

I meant spontaneous, not simultaneous. Sorry. That term is key. Without that term Clausius' statement would be blatantly false. Refrigerators and air conditioners do transfer heat from a cool environment to a warmer one. Work is needed to accomplish this trick.

Think of "spontaneously" as meaning "without external influences." Gravitation is the external influence in this particular problem.

 

[striphe]

I considered that spontaneously meant without work being applied.

In general heat pumps require work to move heat energy from a colder location to a hotter location.

I guess spontaneously is a broad enough to allow it to hold in this situation and others that are similar.

My consideration is that the reasoning behind such a statement, is the fact that a heat gradient can be used to extract 'useful energy' from heat energy. If a heat gradient forms without the input of 'useful energy' then using the heat gradient to extract 'useful energy' would lower entropy.

So I guess we are back at part B of the hypothesis. I would have to conclude that experiment two would generate energy against the second law of thermodynamics, if there would exist variable heat gradients for different materials at the same height. But as this would defy the 2nd law, i would probably place my money on a heat gradient being the same regardless of the material.

Just because I think it is likely, doesn't mean that I don't want to know how to calculate such a heat gradient to make sure that this is the case.

Can anyone do these calculations?