Can Altitude Hypothesis Challenge the Second Law of Thermodynamics?

[D H]

Some kind would, yes. The Earth is not in thermal equilibrium with its environment. The core is about 5700 K, and were it not for the Sun, the external environment temperature would be 2.725 K (the CMB temperature). The temperature gradient in the atmosphere is just an extension of the temperature gradient of the Earth as a whole. The gradient will cease to exist when the Earth's core finally cools to 2.725 K.

 

[striphe]

In terms of a long tube full of a gas?

 

[D H]

How tall is your tube?

If it's only as tall as a building, a tall, tall building at that, there will be too many other factors coming into play.

 

[striphe]

5,000,000 metres say

 

[RonL]

How tall is your tube?

If it's only as tall as a building, a tall, tall building at that, there will be too many other factors coming into play.

Hope this is not too much of an intrusion, but can this not be mimicked in a small condensed way ? If the tube is coiled in some length and placed inside a tank, each end of the tube is flow controlled with vane units, one acting as a compressor and the other acting as an expansion device, the pressure gradient between them will be set only by the mechanical and materials limits.

In my mind this is what I'm seeing, with a few added controls and conditions, heat can be exchanged in and out of the system.

Ron

 

[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.