Can Altitude Hypothesis Challenge the Second Law of Thermodynamics?

[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?

 

[D H]

So I guess we are back at part B of the hypothesis.

Which hypothesis? This one?

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.

You haven't specified how you are going to utilize this temperature difference. No matter how you do it, you will not be violating the laws of thermodynamics (which includes conservation of energy). Let's look at your two column system (posts 23 & 23). Suppose you have two isolated columns containing gases, each a couple of kilometers high. Fill one with hydrogen, the other with xenon, such that at the bottom of each column the pressure is 1 atmosphere and the temperature is 300 K. Note: The column of xenon can't be all that tall because xenon has a very low specific heat and therefore the temperature gradient will be phenomenally steep 61.96 K/km with g=9.81 m/s² throughout. (The temperature gradient in the hydrogen column will only be 0.6858 K/km).

With this, the temperatures at the top of the 2 km towers will differ by 122.55 K. Not a huge difference, but any difference will suffice for a heat engine. So, let's "break the seal" at the top of the columns to take advantage of this difference. We'll be transferring heat from the top of the hydrogen column to the top of the xenon column, stealing some of that transferred heat in the form of useful energy. What's going to happen in the columns? Simple: The lapse rates will no longer be adiabatic. The hydrogen column will have a super-adiabatic lapse rate while the xenon column will have a sub-adiabatic lapse rate. Eventually the two columns will stabilize with equal temperatures at the tops of the columns. Our heat engine of course will become worthless at this point.

Before this happens, let's see if we can take advantage of what is happening at the bottoms of the columns. The xenon column will be warmer at the bottom than will the hydrogen column. So, let's break the seal there as well and install another heat engine. Have we got a perpetual motion machine? Nope. Eventually we'll get equal temperatures at the top and the bottom as well. There ain't no such thing as a free lunch in thermodynamics.

Another what if game: Let's force the bottoms to have a common temperature of 300 K, forever. Now we can draw energy at the top of the column, forever. Is this a perpetual motion device? Nope. That forcing at the bottom requires an energy input, and this energy input will be greater than the amount of energy we can draw out at the top. So once again, no free lunch.

 

[striphe]

It was my consideration that if the bottom of the tubes were the same temperature than the top would have a different temperature and vise versa.

The environment at the bottom has a temperature of 300 K and we have a tube of hydrogen and one of xenon 2km high. Let's consider that these heat engines when inactive insulate the tubes perfectly and that the engines are activated at choice.

Initial conditions, bottom of tubes the same temperature and the tops vary. The heat engines connecting the tube extracts energy as they converge to the same temperature as heat moves from the hydrogen to the xenon. Once the temperatures have converged the heat engine at the top is deactivated. My consideration holds that the temperature of the hydrogen column at the bottom is colder than the environment and the xenon column has a temperature at the bottom that is hotter than the environment. The two heat engines at the bottom then are activated, with heat moving from the environment into the hydrogen column and heat moving from the xenon column into the environment.

The bottom of the columns reach the same temperature as the environment. The heat engines are deactivated at the bottom returning the devise to its initial conditions.

So when you consider that the devise operates in bursts, both mine and your considerations defy the second law of thermodynamics. Unless I've misunderstood.

 

[D H]

Still no violation of the second law. Here:

The bottom of the columns reach the same temperature as the environment.

What environment? By saying that you are making this a non-isolated system. Once you do that you have to account for energy and entropy transfer with the external environment.

While there are more detailed versions of the second law that take into account interactions with the external environment, the simplistic version of second law of thermodynamics embodied by dS/dt \ge 0, and Clausius' statement in particular, pertains to isolated systems only.

 

[striphe]

So the device would operate as I've depicted it, but wouldn't defy the second law of thermodynamics because it isn't an isolated system?

 

[D H]

I didn't say that. You have a column that is made of some substance that is a perfect insulator and reflector. Unobtainium, in other words.

It appears you are actively trying to find a way to violate the laws of conservation of energy and the laws of thermodynamics. If that is the case, this is not the site to carry on such discussions.

 

[striphe]

It's all theoretical. Giving things perfect properties just makes things less complex, but none the less relevant.

The heat gradient formed by gravity and the second law of thermodynamics, weren't compatible in my understanding and this post is an attempt to rectify my understanding.

No one has explained how these are compatible as of yet.

My understanding doesn't highlight a conservation of energy defiance, maybe this is key.
Can you elaborate on how this is defied in the thought experiment?

 

[D H]

But you are making things overly complex, striphe. Rube Goldberg devices do not in general help understanding. All they are good for is annoying students (some profs revel in coming up with overly complex problems) and befuddling patent examiners (the over unity devices that erroneously manage to receive a patent are almost inevitably overly complex devices in which it is hard to see the flaw).

 

[striphe]

So how would you display the issue to make it less complex and more approachable?

I've honestly tried to make it as simple as I could, but i understand that doesn't mean that it is the simplest it could be.

 

[striphe]

How is two long tubes and three heat engines overly complex?

 

[Smacal1072]

Which hypothesis? This one?



You haven't specified how you are going to utilize this temperature difference. No matter how you do it, you will not be violating the laws of thermodynamics (which includes conservation of energy). Let's look at your two column system (posts 23 & 23). Suppose you have two isolated columns containing gases, each a couple of kilometers high. Fill one with hydrogen, the other with xenon, such that at the bottom of each column the pressure is 1 atmosphere and the temperature is 300 K. Note: The column of xenon can't be all that tall because xenon has a very low specific heat and therefore the temperature gradient will be phenomenally steep 61.96 K/km with g=9.81 m/s² throughout. (The temperature gradient in the hydrogen column will only be 0.6858 K/km).

With this, the temperatures at the top of the 2 km towers will differ by 122.55 K. Not a huge difference, but any difference will suffice for a heat engine. So, let's "break the seal" at the top of the columns to take advantage of this difference. We'll be transferring heat from the top of the hydrogen column to the top of the xenon column, stealing some of that transferred heat in the form of useful energy. What's going to happen in the columns? Simple: The lapse rates will no longer be adiabatic. The hydrogen column will have a super-adiabatic lapse rate while the xenon column will have a sub-adiabatic lapse rate. Eventually the two columns will stabilize with equal temperatures at the tops of the columns. Our heat engine of course will become worthless at this point.

Before this happens, let's see if we can take advantage of what is happening at the bottoms of the columns. The xenon column will be warmer at the bottom than will the hydrogen column. So, let's break the seal there as well and install another heat engine. Have we got a perpetual motion machine? Nope. Eventually we'll get equal temperatures at the top and the bottom as well. There ain't no such thing as a free lunch in thermodynamics.

Another what if game: Let's force the bottoms to have a common temperature of 300 K, forever. Now we can draw energy at the top of the column, forever. Is this a perpetual motion device? Nope. That forcing at the bottom requires an energy input, and this energy input will be greater than the amount of energy we can draw out at the top. So once again, no free lunch.

In your last thought experiment, suppose instead of forcing the bottoms to have a common temperature of 300 K, we just connect the bottoms with a thermally conductive metal, like copper.

If we "run" the heat engine at the top at a rate slower than that at which the system comes to hydrostatic equilibrium, do we get a free lunch then?

 

[D H]

Whether a device is simple Carnot heat engine or a complex Rube Goldberg contraption, there is no free lunch in thermodynamics. Conservation of energy says ignoring losses, the best you can possibly do is break even. Entropy concerns say you cannot ignore losses.

There ain't no such thing as a free lunch -- particularly in thermodynamics.

 

[striphe]

Although its easy enough to say we won't get a free lunch, as the second law doesn't allow for free lunches. It seems excessively difficult to explain how such is true in with these hypothetical devises.

The principle of all these hypothetical devises are based on the seeming overlook (at least what I've seen) by thermodynamics to consider that a temperature differences will arise in a body of gas under the force of gravity or simulated gravity (centrifugal force).

Any number of devises that attempt to take advantage of this particular temperature difference could be conceived. I expect what ever argument against one will wipe them all out. But the inability of users to cope with either the 'complexity' of these devises and the fact that there is a temperature difference induced within a body of gas, has gotten physics no closer to dismissing these devises, with what I would consider a required explanation.

 

[klimatos]

The atmosphere's heat budget shows that it receives some 102 watts per square meter of solar insolation, some 268 watts of terrestrial radiation, roughly 17 watts by conduction from the warmer surface, and a final 3 watts by hydrologic cycling (water evaporates from the warm surface higher temperatures than it condenses at in the atmosphere). Thus, an average of 74% of its heat comes from the surface of the Earth.

When a parcel of air sinks, more molecules have a downward component of motion than have an upward component. The opposite is true when a parcel of air is forced up (nothing moves against the force of gravity unless pushed by a stronger force). Gravity accelerates downward molecular motions and decelerates upward motions. Changes in mean molecular velocities are measured as changes in temperature. Thus, sinking air warms and rising air cools.

 

[klimatos]

The principle of all these hypothetical devises are based on the seeming overlook (at least what I've seen) by thermodynamics to consider that a temperature differences will arise in a body of gas under the force of gravity or simulated gravity (centrifugal force).

Could you cite a source for this development of temperature differences in a parcel of gas at equilibrium under the influence of gravity as it sole outside force. Differences in density: yes. Differences in temperature: no way. At NTP, each gas molecule collides and exchanges kinetic energy more than five billion times a second. We measure this mean kinetic energy of translation as temperature. The mathematical probability that some significant potion of a gas would develop a temperature difference from the rest without some outside force other than gravity is incredibly small. Statistical mechanics tells us that for all intents and purposes it just isn't going to happen.

 

[striphe]

klimatos, my support of the temperature difference is based on the understanding that, if molecular collisions were the only way heat was being transferred within a body of gas, then particles moving down speed up and particles moving up slow down; resulting in a temperature gradient. But heat energy can be transferred through em radiation which wouldn't be affected by such a force in classical physics.

I consider it plausible that the em radiation may even out the temperature in a closed body of gas.

As D H has given quantitative calculations as to the temperature difference within a closed and static body of gas and that he is the most senior member of the forum posting on this thread; it gives me a lot of confidence that the temperature difference does arise.

When it comes down to it, I will sway to the side with the most evidence and rationale. Science and stubbornness are incompatible.

 

[D H]

Could you cite a source for this development of temperature differences in a parcel of gas at equilibrium under the influence of gravity as it sole outside force. Differences in density: yes. Differences in temperature: no way.

Yes way. It's called "lapse rate" (google that term). Here is a plot of the dry and moist adiabatic lapse rates:

http://www.fas.org/irp/imint/docs/rst/Sect14/moist_dry.jpg

Here is a largish (17.1 MB) reference:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf

Although its easy enough to say we won't get a free lunch, as the second law doesn't allow for free lunches. It seems excessively difficult to explain how such is true in with these hypothetical devises.

Since you are the one making the extraordinary claim, striphe, the burden of proof falls upon you to prove that such a device would allow a violation of the second law of thermodynamics. You are assuming that the gases in these columns will follow adiabatic conditions. They won't. You are forcing conditions to be other than adiabatic, so the temperature profile will be something other than adiabatic.

 

[Smacal1072]

Striphe, you might want to simplify your analysis by considering an ideal gas.

If you consider a monatomic, ideal gas (like Xenon), then you can assume that when a gas atom travels upward in the tube, it loses energy due to increasing it's gravitational potential energy. You can make your idea more concrete by calculating how much kinetic energy a particle loses by traveling upwards against gravity using something like 1/2kT - mgh (for some reason latex won't work...)

HOWEVER, you should read this paper:

"On a paradox concerning the temperature distribution of an ideal gas in a gravitational field" by S Velasco, F L Román and J A White.

I didn't read the whole thing, but I believe they resolve the paradox by showing that the coldest atoms in the maxwell-boltzmann distribution don't have enough energy to travel far up the tube, so that while all the atoms lose energy as they travel upwards, by shedding the coldest atoms, the temperature in fact doesn't change as we move upwards in the tube.

 

[klimatos]

Yes way. It's called "lapse rate" (google that term). Here is a plot of the dry and moist adiabatic lapse rates:

As a retired professor of atmospheric sciences, I am familiar with lapse rates. I referred to a closed system at equilibrium. Adiabatic lapse rates are phenomena of moving air--not an equilibrium situation. The normal atmospheric lapse rate is an artifact of the Earth's heat budget. It would not exist without an outside source of energy--the Sun.

 

[klimatos]

klimatos, my support of the temperature difference is based on the understanding that, if molecular collisions were the only way heat was being transferred within a body of gas, then particles moving down speed up and particles moving up slow down; resulting in a temperature gradient. But heat energy can be transferred through em radiation which wouldn't be affected by such a force in classical physics.

I consider it plausible that the em radiation may even out the temperature in a closed body of gas.

Under conditions of equilibrium, the number of molecules having a downward component of motion is essentially the same as the number of molecules having an upward component of motion. Gravitational energy gains match gravitational energy losses, and no temperature gradient emerges.

Heat (enthalpy) transfer within a gas may be accomplished by any or all of the three classical methods: molecule-to-molecule electromagnetic radiation, molecule-to-molecule conduction (collisions) and mass transfer (fluid flow). Under conditions of equilibrium, fluid flow is ruled out but the other two remain. Most of the heat transfer in the Earth's atmosphere is brought about by electromagnetic radiation rather than conduction.

 

[klimatos]

As D H has given quantitative calculations as to the temperature difference within a closed and static body of gas and that he is the most senior member of the forum posting on this thread; it gives me a lot of confidence that the temperature difference does arise.

Can you give me a posting number for these calculations? I would like to read them.

 

[striphe]

Post number 71

D H hasn't given full calculations but has provided the results of calculations.

 

[klimatos]

I didn't read the whole thing, but I believe they resolve the paradox by showing that the coldest atoms in the maxwell-boltzmann distribution don't have enough energy to travel far up the tube, so that while all the atoms lose energy as they travel upwards, by shedding the coldest atoms, the temperature in fact doesn't change as we move upwards in the tube.

There seems to be quite a bit of misunderstanding of kinetic gas theory and statistical mechanics throughout this thread. A molecule that is at the bottom of the tube now is still likely to be at the bottom of the tube a minute from now. At NTP a molecule changes its translational speed and direction more than five billion times a second. Its path over that second can be described as a random walk. It is no more likely to go up than it is to go down, and its direction of movement is independent of its translational velocity.

If you want to give a molecule a "temperature" based on this translational velocity, then consider that in that single second that molecule will have changed its temperature some five billion times--more or less. The Maxwell-Boltzmann distribution of molecular velocities not only applies to a population of molecules; it also applies to the distribution of speeds of a single molecule over any significant portion of time.

Therefore, the idea of a "cold" molecule being less likely to go up the tube is meaningless. It is not the physical molecules themselves that conduct thermal energy, it is the impulses that they generate at collisions. These impulses travel up and down the tube at roughly the speed of sound, while the actual migration of molecules is a matter of self-diffusion.

 

[Smacal1072]

Hi klimatos,

I absolutely agree with you - However, the paper I mentioned doesn't deal with gases at NTP, it only discusses an apparent paradox involving ideal gases.

 

[JaredJames]

Hi klimatos,

I absolutely agree with you - However, the paper I mentioned doesn't deal with gases at NTP, it only discusses an apparent paradox involving ideal gases.

Gonna stick my neck out here, but I was under the impression ideal gases don't exist? So any paradox doesn't either?

 

[klimatos]

Gonna stick my neck out here, but I was under the impression ideal gases don't exist? So any paradox doesn't either?

Of course you're right, Jared. Ideal gases don't exist. They are usually either teaching devices for teachers or speculative devices for scholars. They are useful in both roles. The atmospheric sciences, for one, would be lost without the concept of the ideal gas.

On the other hand, a large number of the threads in this section seem to deal with idealized situations and hypothetical devices.

Jared, I think you're just having fun!

 

[JaredJames]

Jared, I think you're just having fun!

But am I wrong?

If you use an 'ideal' situation for analysis, it could certainly violate the laws of thermodynamics (PMM's when ignoring friction losses for example).

So just because under perfect conditions you can violate a law, if those conditions can never exist then there's no problem.

You can ignore friction to help make a problem easier, but that doesn't mean you can apply the same thinking all the time and extend it to other areas - which is why you end up with perpetual motion devices.

 

[striphe]

One can understand that under ideal conditions a wheel that experiences no friction can spin forever or that entropy won't increase in a number of hypothetical occurrences.

This is different, we have something reducing entropy; which I would say is impossible in ideal circumstances according to the second law of thermodynamics.

In a closed static body of gas, under the force of gravity there is going to be a pressure difference. As one is dealing with a gas, there are less particles per volume at the lower pressure end then the higher pressure end.

If there is less particles at the lower pressure end, each gas particle has to be moving faster for the temperature be the same throughout the body. Can someone explain how this would be so?

 

[D H]

As a retired professor of atmospheric sciences, I am familiar with lapse rates. I referred to a closed system at equilibrium. Adiabatic lapse rates are phenomena of moving air--not an equilibrium situation. The normal atmospheric lapse rate is an artifact of the Earth's heat budget. It would not exist without an outside source of energy--the Sun.

You have this exactly backwards. The adiabatic lapse rate is a direct consequence of the second law of thermodynamics. A lapse rate that deviates from the adiabatic lapse rate is a phenomena of moving air.

 

[klimatos]

If there is less particles at the lower pressure end, each gas particle has to be moving faster for the temperature be the same throughout the body. Can someone explain how this would be so?

A gas can have the same temperature at a wide variety of pressures. Temperature measures the mean kinetic energy of translation of the gas molecules. It is an average. T= (mv^2)/k, where T is the temperature, m is the molecular mass, v is the root-mean-square molecular velocity along a single axis of movement, and k is Boltzmann's Constant.

Pressures, on the other hand, are usually a function of both temperature and molecular number density: P = nkT, where n is the number density. Pressure is a total. It is the number of molecular impacts times the mean impulse transferred per impact.

 

[striphe]

This doesn't answer the question of how the molecules have a higher average velocity at the top than the bottom.