Can Altitude Hypothesis Challenge the Second Law of Thermodynamics?

[striphe]

Hypothesis
A contained body of gas that is within a field of gravity will have differing temperature in differing locations within the body. These differing temperatures can be utilised to by a heat engine, to convert heat energy into other forms.

Background
Heat can be described as the disordered vibrations and movements of molecules. Even though it is differentiated from the other forms of energy, it is essentially an unordered form of kinetic energy.

In a gaseous state, molecules are free to move with and against gravity. When they move with gravity they gain more velocity, increasing the contribution of energy that the particular molecule gives as heat energy in that particular location it enters. When they move against gravity they lose velocity, decreasing the contribution of energy that the particular molecule gives as heat energy in the particular location it enters.

This is apparent in everyday live when you consider that it is generally colder in a tall mountain than at sea level as the gas molecules lose heat energy as they move to higher altitudes.

The very important distinction must be made that moving an perfectly insulated contained body of gas to a higher altitude will not cool the gas, as the gas has not been transported to the location by its heat energy, but by mechanical energy applied to the container.

Thought Experiment 1
This hypothesis is best understood when depicted in a thought experiment.

Imagine a very tall structure ascends from a hot desert into the sky, to a point where it is so cold that a bottle of water would freeze at the top. This structure supports an elevator style mechanism that is of the highest efficiency, which lifts a device and drops a device that is exactly the same simultaneously. The result is that if one device is lifted to the top of the structure, the other rests at the bottom in the hot desert.

These devices are large bodies of water that are perfectly insulated, with the addition of reversible heat engine, that when activated will connect the insulated body of water and the outside world.

The device at the top of the structure is at the same temperature as its surroundings and the one at the bottom is at the same temperature as the hot desert. The elevator is activated and the devices swap position. As both bodies of water are insulated they are not the same temperature as their surroundings anymore. The heat engines are activated allowing the heat of the desert to enter the cold body of water and the heat of the other body of water to disperse into high altitude. During this process the heat engines extract the maximum amount of energy from the heat gradients until both bodies are at equilibrium with their surroundings. This process can then be re conducted.

Issue
I assume that the moving of the devices could approach almost 100% efficiency theoretically with the heat engines approaching Carnot efficiency. Based on this assumption, the energy extracted from the heat engines is greater than the loss caused by changing the positions of the sub-devices, this device could perpetuate.

Replacing the atmosphere with a long insulated container of gas. The device would not be able to perpetuate as it would absorb the heat energy from the system reducing it to a point where the device could no longer perpetuate. In this instance however, the system has reduced entropy.

Such an assumption would contradict the second law of thermodynamics.

 

[rcgldr]

There are somewhat similar devices used to harness some amount of energy from the ocean via very tall pipes, but I'm not sure how much the difference in salinity as well as temperature versus depth plays a role.

 

[alxm]

Hypothesis
A contained body of gas that is within a field of gravity will have differing temperature in differing locations within the body.

Wrong.

In a gaseous state, molecules are free to move with and against gravity. When they move with gravity they gain more velocity, increasing the contribution of energy that the particular molecule gives as heat energy in that particular location it enters. When they move against gravity they lose velocity, decreasing the contribution of energy that the particular molecule gives as heat energy in the particular location it enters.

Wrong. The energy gets continually re-distributed in the intermolecular collisions. That's how diffusion works. And the potential energy difference is ridiculously tiny compared to a gas molecule's kinetic energy. By that kind of reasoning, we should all suffocate since the heavier CO2 in the atmosphere should collect at ground level.

This is apparent in everyday live when you consider that it is generally colder in a tall mountain than at sea level as the gas molecules lose heat energy as they move to higher altitudes.

No, that's not why it's colder at altitude. It's colder at altitude because you're farther away from a warm body, namely the earth.

 

[Sakha]

It not perpetual motion machine in any sense, the 'extra' energy you see comes from the desert being heated by the sun.

 

[striphe]

i get what you are saying alxm, heat does diffuse throughout the the body and that the difference in heat on Earth is partially due to the the source of heat. However when you consider mountains, they are close to the warm body, as the high altitude surroundings are absorbing the em radiation given off by the sun.

You stated that gravity would affect the temperature of particular locations with in a given body, just not significantly. If I changed the location of the thought experiment from Earth to a more massive planet I would consider that this effect would become more significant, would you not also?

rcgldr, interesting device. do you have a link to some info on it?

Sakha, I would defiantly agree with the heat source reasoning, if one can highlight that in no way does gravity induce a heat difference within a body of gas.

Now I am wondering that if hypothetically a long piece of copper wire was placed against the structure in the thought experiment, with the entire piece covered in a perfectly heat insulating material except for a small length at the end on to of the structure. If one left this for a significant amount of time and then cut the wire at the bottom, exposing some copper, so that one could measure the temperature of the copper. Would the copper at the bottom, be as cold as the top?

 

[alxm]

i get what you are saying alxm, heat does diffuse throughout the the body and that the difference in heat on Earth is partially due to the the source of heat. However when you consider mountains, they are close to the warm body, as the high altitude surroundings are absorbing the em radiation given off by the sun.

Why are you even trying to debate this point? It's a simple fact that gravity has nothing to do with why it's cold farther up in the atmosphere. And mountains are colder because a 'mountain' is by definition a protrusion of the Earth's surface up into higher, colder, altitudes, where the layers of air are - on average - much farther from the earth.

You stated that gravity would affect the temperature of particular locations with in a given body, just not significantly.

No, I did not say that.

 

[rcgldr]

Wiki article about solar updraft tower:

http://en.wikipedia.org/wiki/Solar_updraft_tower

Ocean thermal energy conversion:

http://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion

Salt fingering: (I'm not sure if this caused the small fountain effect I saw in an old television show, related to perpetual salt fountain):

http://en.wikipedia.org/wiki/Salt-fingers

Not sure if perpetual salt fountains ever were useful, since wave powered tall vertical tubes in the ocean with one way valves would probably be more efficient.

http://gcaptain.com/maritime/blog/tubes-in-the-ocean-→-bizarre-marine-technology

 

[striphe]

Can anyone explain why a closed body of gas will have no variance in temperature in detail if subjected to gravity?

thank you for the links, rcgldr

 

[striphe]

have a read of the link below alxm

http://www.physlink.com/education/AskExperts/ae670.cfm

 

[alxm]

have a read of the link below alxm

http://www.physlink.com/education/AskExperts/ae670.cfm

Oh look! Someone else made the same erroneous claim on the internet! It must be true! (ooh and he's a BSEE.. That says a lot, given we all know how much atmospheric thermodynamics is in the EE curriculum these days!)

Air temperature goes down with elevation due to increased distance from the earth. The atmosphere is heated by the Earth, not vice-versa. This holds up to the tropopause, after which, in the stratosphere, the temperature then increases with height again, due to conduction downwards from the ozone layer, which is heated by solar UV.

Need I go on, or is this enough to convince you your 'hypothesis' has no basis in reality, and doesn't even come close to describing how the temperature changes with altitude?

 

[cjl]

There is actually some truth to that claim. It isn't the basis for the Earth's temperature gradient, but it is true that as a parcel of warm air rises, it will expand and cool, and this causes a natural maximum temperature gradient that the atmosphere can have (as if the temperature gradient becomes steeper than this, then convection will dominate the heat transfer into the upper atmosphere, which flattens the temperature gradient back down to this level).

For more info, look up "Adiabatic lapse rate". The lower atmosphere of Venus has a temperature gradient driven primarily by this, as do gas giants.

 

[striphe]

Im aware that temperature does not just simply drop with altitude, due to uv absorbtion. What i said is not the absolute reason as to why there is a difference in temperature within the atmosphere, but it does play a part. So how does one rule out the issue in the first post?

Alxm can you find something that backs up your points?

 

[cjameshuff]

Can anyone explain why a closed body of gas will have no variance in temperature in detail if subjected to gravity?

Without an external source of energy, every closed system will equalize in temperature as it approaches equilibrium. Can you give any reason why this would be different when gravity is involved? Any reason at all to think such an effect exists? (And as has already been pointed out, planetary atmospheres are not such a reason.)

 

[striphe]

why is gravity factored into lapse rate?

 

[D H]

Wrong.

No, you are wrong.

No, that's not why it's colder at altitude. It's colder at altitude because you're farther away from a warm body, namely the earth.

Yes and no. It's cooler at altitude because air is in general a poor conductor of heat, a poor absorber of heat and because pressure decreases with altitude. That air does conduct heat to some extent and that the atmosphere does absorb some of the incoming sunlight mitigates the effects of altitude. The environmental lapse rate is considerably less than the dry adiabatic lapse rate.

Why are you even trying to debate this point? It's a simple fact that gravity has nothing to do with why it's cold farther up in the atmosphere.

Wrong again. At least you are consistent.

 

[Bob S]

There is actually some truth to that claim. It isn't the basis for the Earth's temperature gradient, but it is true that as a parcel of warm air rises, it will expand and cool, and this causes a natural maximum temperature gradient that the atmosphere can have (as if the temperature gradient becomes steeper than this, then convection will dominate the heat transfer into the upper atmosphere, which flattens the temperature gradient back down to this level).

For more info, look up "Adiabatic lapse rate". The lower atmosphere of Venus has a temperature gradient driven primarily by this, as do gas giants.

Exactly.
Air pressure varies with altitude due to gravity. Temperature varies with altitude due to air pressure difference and adiabatic expansion (adiabatic lapse rate 9.8 degrees C per kilometer). See

http://farside.ph.utexas.edu/teaching/sm1/lectures/node56.html

In Death Valley National Monument (California), it is possible to stand on Telescope Peak (elev. +3366 meters) on the west side and directly look down at Badwater (elev -85 meters) where the air temperature is ~ 30 degrees C higher. As the air blows up the east side of Death Valley to Dante's View (elev ~ +1700 meters), it cools again, due to the adiabatic lapse rate of ~ 9.8 degrees C per kilometer.

Bob S

 

[D H]

Without an external source of energy, every closed system will equalize in temperature as it approaches equilibrium. Can you give any reason why this would be different when gravity is involved? Any reason at all to think such an effect exists? (And as has already been pointed out, planetary atmospheres are not such a reason.)

As has already been pointed out, the pressure gradient in the Earth's lower atmosphere is the primary reason why temperature decreases with increasing altitude. As BobS already pointed out, the dry adiabatic lapse rate is 9.8 C per kilometer. This is explained solely by assuming that (a) air does not absorb or lose energy from sunlight or from the surrounding air (that's why this is called the adiabatic lapse rate), and (b) the atmosphere is in hydrostatic equilibrium.

The true lapse rate is typically less than the adiabatic lapse because assumption (a) is not always true. Extremely humid air releases heat as water vapor condenses to form water droplets. Humid air is not transparent in the infrared, so it also absorbs energy from sunlight. Another example: Ozone absorbs energy from sunlight, which is why the lapse rate is positive in the stratosphere.

Above the stratosphere the assumption of hydrostatic equilibrium fails. This thread however is not about the upper atmosphere.

 

[striphe]

If I break the hypothesis into two parts:
(a) A contained body of gas that is within a field of gravity will have differing temperature differing locations within the body.
(b)These differing temperatures can be utilised to by heat engine, to convert heat energy into other forms.

Part A appears to be confirmed by the more senior users who have posted.

So two questions remain:
(1) Is part B valid?
(2) Is the hypothesis in violation of the second law of thermodynamics?

 

[D H]

Part A is correct, but only on a very, very large scale. On a small scale (house or building size is small) the temperature can and does rise with increased height. Remedying this is why people install ceiling fans in their houses.

Part B, I don't think so. Suppose you make a container that is very, very tall and very well insulated, heated only from the bottom. Fill it with dry air and let it come to equilibrium. The resulting temperature gradient that results will be the minimum energy configuration of the column. Just because there is a temperature gradient does not necessarily mean that usable energy can be extracted from the column.

 

[striphe]

So considering thought experiment one, where do you think its shortcomings are?

also would the temperature gradient differ for different gases?

Would a temperature gradient exist for solids and liquids?

 

[Bob S]

So considering thought experiment one, where do you think its shortcomings are?

also would the temperature gradient differ for different gases?

Sure, for a mono-atomic gas like helium, neon, or argon instead of air.

Bob S

 

[striphe]

Assumptions
(a) different materials (solid, liquid or gas) will vary in the amount by which gravity will form a temperature gradient within the body.
(b) although a temperature gradient forms, heating/cooling a material (solid, liquid or gas) in a given location will result in heating/cooling the entire material.

Thought experiment two
two different materials (solid liquid or gas) are placed into very long pipes. These pipes are insulted with a perfect insulator and are capped at each end by a thermally conductive material. The selection of the two materials placed into the capped pipes is based on the temperature gradient that forms due to being subject to the force of gravity. Pipe X has a material within it that results in the least possible heat gradient forming. Pipe Y has a material that results in the maximum heat gradient forming.

These two pipes have one end capped over the top of the heat conductor a perfect insulator. The pipes are then placed next to each other in a vertical position, with the insulated ends at the top. As at the bottom the two ends of the pipe are conductive to heat, both ends should be in equilibrium (eventually at least) with the external environment at that altitude and with each other at those ends.

At the top, pipe X will be hotter than pipe Y, based on the materials resulting in differing temperature gradients. Now the apparatus has three Carnot heat engines added to it. One connects the two top ends, with the other two, each placed on the bottom end of each pipe. The heat engine at the top would absorb part of the heat energy as it moves across from the top of pipe X to the top of pipe Y, until they reach equilibrium.

The configuration however does not allow equilibrium to be reached. As the top of pipe Y gets hotter, that heat is conducted down to the bottom resulting in the bottom of pipe Y being hotter than the external environment. The reverse occurs for the bottom of pipe X, the top is cooled and heat is conducted from the bottom of pipe X resulting in the pipe being cooler than the external environment. The heat engines at the bottom make use of the gradients formed between the external environment and the bottom ends of the pipe.As the top end moves towards equilibrium it induced disequilibrium between the external environment and the two bottom ends, which in turn moves the top ends back to disequilibrium as the move towards equilibrium. The result is system that can not achieve equilibrium and an apparatus that lowers entropy.

Additional comments
Its best assumed that at least one of the assumptions (highlighted or hidden within) is wrong. Thought experiment one doesn’t rely on assumption A, but on the assumption that the mechanical component of the device used to move the heat engines and sinks could theoretically approach 100% efficiency or at least an efficiency that would result in more energy being harnessed from the device than spent in its mechanical components. My confidence in assumption B is very high.

Also, would a centrifuge, induce a heat gradient?

Feel free to put your two cents worth in (sources would be appreciated).

 

[striphe]

Iv attached a basic diagram so you can understand these thought experiments. On the left is thought experiment one and on the right is thought experiment two.

Thermodynamics infers to me that a closed system will enter thermal equilibrum eventually, but my vague understanding of the atmosphere contradicts this when i consider that gravity would maintian a heat gradient.

Im only trying to resolve the problems in my understanding, as they result in contradictions.

Can anyone resolve them?

 

[cjameshuff]

As has already been pointed out, the pressure gradient in the Earth's lower atmosphere is the primary reason why temperature decreases with increasing altitude.

striphe has repeatedly made it clear he's talking about a closed system. Again, planetary atmospheres do not qualify. Earth's atmosphere is simply not a closed system, it has a constant input of energy from the sun that is absorbed mainly at the surface. The gravity field affects transport of heat, but it doesn't itself cause a temperature difference.

(ignoring relativistic effects due to gravitational redshift that would be extremely minor at Earthly scales, and still not a way to get energy from gravity)

 

[striphe]

If all assumptions were correct, then one wouldn't be obtaining energy from gravity but rather, using gravity to absorb heat energy and create a heat gradient. The energy harnessed would come from heat energy.

My doubt is increasing more in first part of the hypothesis.
"Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell-Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. Thermal equilibrium of a system does not imply absolute uniformity within a system; for example, a river system can be in thermal equilibrium when the macroscopic temperature distribution is stable and not changing in time, even though the spatial temperature distribution reflects thermal pollution inputs." this is from a wiki page.

The particular part "This outcome allows a single temperature and pressure to be attributed to the whole system." I don't fully understand, as when subjected to gravity a body of gas will have pressure variation.

The relationship with temperature and pressure is easy to understand in a gravity free environment. One mole of gas with a specific heat content, if place in two different containers, one larger than the other. The larger will have less pressure and temperature than the smaller container.

One could assume with simple reason that in a gravity affected container, that the lower pressure top would have a lower temperature and that the higher pressure bottom would have a higher pressure bottom. Simple reason however isn’t always adequate reason.

For there to be equal temperature at the top of a gravity affected body, the kinetic energy of each particle would have to be on average the same at any position within the vessel. Ignoring em-radiation this would be impossible. Ignoring the effects of modern relativity one could see how it could be possible, as more em-radiation would be emitted from the hotter bottom causing the colder top to heat up until temperature equilibrium emerges. But then adding relativistic effects would then make it impossible, I assume as em-radiation is in its own right affected by gravity, lowering the energy contribution of up moving em-radiation and increasing the contribution of down moving radiation to a molecule.

Relativistic effects do affect the efficiency of the mechanical component of device one; as the hotter one of the sinks has more mass, based on energy mass equivalence. One is always lifting the hotter sink; the mechanical devise cannot achieve 100% even theoretically.

I am unsure if in experiment one the minor energy gain would be equivalent to the minor energy loss.

It would be good to come to some kind of consensus on this.

 

[Phrak]

I don't wish to become embroiled in this discussion, however I will attempt to answer the following: Why does a column of gas in a gravitational field not allow extraction of energy in defiance of the conservation of energy where the energy extraction may be considered small compared to the bulk of the gas energy? (Or, please tell me why my perpetual motion concept is right or wrong.)

Bernoulli's Equation helps. This is an equation where the energy of a parcel of gas depends upon its velocity, gravitational potential and pressure. For the problem at hand we don't care about the velocity and consider it zero at any altitude.

We prepare a column of gas in a gravitational field, filling from bottom to top. When filled the pressure is less at the top thus increasing its kinetic energy. The kinetic theory of gasses tells us that the temperature is also lower the higher we go. The velocity of each molecule is, on average, less at the top than the bottom. This is balanced by an increase in gravitational potential energy.

So we put a thermal pile in each end of the column and we can extract energy from the temperature difference.

So what gives? Why isn't this a perpetual motion machine? We can extract energy. And if the thermal piles cause the gas temperature to equalize then we just cycle the gas through a loop to get the temperature gradient back.

If anyone attempts to claim that conduction will eventually even out the temperature this would be thwarted by thermally insulating gas parcels from energy exchange. Who can answer?

 

[TheRealTL]

The heat engine is shown in the form of wind or water currents. So a fan blade is what we use to "capture" this energy.

One of the guys in the this thread got it right. A tube of gas will eventually equalize its pressure and the heat engine will stop working. The difference in temperature at different altitudes is due to fewer impact events on a system due to fewer particles available at higher altitudes.

You can recreate this effect very easily by taking a tube of gas and putting one half in water and the other in air. There will be a small wind effect until the tube gas equalizes.

 

[striphe]

http://en.wikipedia.org/wiki/Stirling_engine

These are the kind of heat engines i was considering for the thought experiments, they can be designed to achieve almost Carnot efficiency.

This kind of heat engine allows the gases or liquids to stay static. With only heat conducting into the device to power it.

These are the assumptions that are required to be true for the thought experiments to defy the second law of thermodynamics (I seriously doubt they are true and i want to know what would actually occur, as current understanding suggests that these situations do theoretically defy this law)

Experiment one:
(a) a heat gradient forms within very long static column of gas
(b) heating or cooling any part of the column of gas will result in heating or cooling throughout.
(c) the mechanical devise used to make use of this heat gradient could achieve an efficiency that would allow it to gain more energy than is lost in the process.

Experiment two
(a) a heat gradient may form within matter when subjected to gravity
(b) different forms of matter can result in different forms heat gradients under the same conditions
(c) heating or cooling any part of the matter will result in heating or cooling throughout.

Sorry I can't answer your questions Phrak. Hopefully someone will soon.

 

[D H]

One of the guys in the this thread got it right. A tube of gas will eventually equalize its pressure and the heat engine will stop working.

The pressure in the atmosphere will indeed eventually equalize -- after the entire Earth cools to the background temperature of the universe, that is.

The pressure gradient results from hydrostatic equilibrium. The same phenomenon explains how liquid barometers work and explains why the pressure at the center of the Earth is so very high. Imagine if the tube was thousands of kilometers tall. The top of the tube will be vacuum, the bottom atmospheric pressure.

 

[striphe]

Would a heat gradient exist?

And if so, would this heat gradient be the same for any matter placed in the tube?

 

[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