Will an atmosphere under the action of gravity assume a linear temperature profile with slope equal to the dry adiabatic lapse rate? Loschmidt said yes, while Boltzmann and Maxwell claimed that the atmosphere would be isothermal. Graeff (2007) has made experiments supporting Loschmidt and so it is natural to seek a theoretical explanation.
Consider a horizontal closed insulated tube filled with still air at uniform temperature. Let the tube be turned into an upright position. Alternatively, we may consider a vertical tube with gravitation gradually being turned on from zero, or a horizontal tube being rotated horizontally starting from rest. During increasing gravitational force the air will be compressed and knowing that compression of air causes heating, we expect to see a temperature increase. How big will it be? Well, the 2nd Law of Thermodynamics states that under adiabatic and isentropic transformation (no external heat source and no turbulent dissipation):
- c_vdT + pdV =0
- pdV + Vdp = RdT
and the equilibrium equation in still air with x a vertical coordinate
- dp = -g rho dx or Vdp = - gdx
where g is the gravity constant, rho = 1/V is density, we find
- (c_v + R) dT = -gdx or c_p dT/dx = - g,
We thus find still air solutions with a dry adiabatic lapse rate dT/dx= - g/c_p = - g with c_p = 1 for air, as a consequence of compression by gravitation, using
- work by compression stored as heat energy
- pressure balancing gravity (hydrostatic balance).
A corresponding family of stationary still air solutions is given by (assuming x = 0 corresponds to the bottom of the tube):
- p(x) ~ (1 - gx)^(a+1)
- rho(x) ~ (1 - gx)^a
- T(x) ~ (1 - gx)
with a >0 a constant. In the absence of heat conduction such solutions may remain as stationary still air solutions. We thus find support of Loschmidt's conjecture of still air solutions with the dry adiabatic lapse rate, in the absence of heat conduction. In the presence of (small) heat conduction, it appears that a (small) external source will be needed to maintain the lapse rate. Of course, in planetary atmospheres external heat forcing from insolation is present.
Returning the tube to a horizontal position would in the present set up without turbulent dissipation, restore the isothermal case. Turning the tube upside down from the vertical position would then establish a reverse lapse rate passing through the horizontal isothermal case.
Returning the tube to a horizontal position would in the present set up without turbulent dissipation, restore the isothermal case. Turning the tube upside down from the vertical position would then establish a reverse lapse rate passing through the horizontal isothermal case.
Further, it seems that without heat source, the isothermal case of Boltzmann/Maxwell will take over under the action of heat conduction, with p(x) ~ exp( - cx) and rho(x) ~ exp ( - cx) with c>0 a constant.
For the Euler/Navier-Stokes equations for a compressible gas subject to gravitation, see Computational Thermodynamics and the chapter Climate Thermodynamics in Slaying the Sky Dragon.
In order to support Graeff and Loschmidt I think you have to start with a vertical isothermal column and then see it turn into the adibatic, which I don't think it will. I think it is important to point out that by erecting the column you add external work to the system, which will be an obvious point of attack from people (you-know-who). But the combined heat source - conduction - convection I think they will have a hard time dismissing off hand.
SvaraRaderaBut if the column is rotated at mass center - slowly?
SvaraRaderaI agree that an initially isothermal vertical cylinder will probably stay isothermal. But I guess the problem is what happens if you suddenly "turn on" gravitation e.g. by starting to rotate it, which would be like erecting a horizontal cylinder (by doing some work).
SvaraRaderaThis question has outlived its usefulness, and competent physicists should not be distracted by the utter inability or refusal of the majority of their fellows to learn the truth, and to be honest. I enunciated the simple truth in November 2010 [here]:
SvaraRadera"The temperature profile of the atmosphere is dictated solely by gravity acting on the ocean of air and the specific heat of the air, which imposes a temperature "lapse rate" (a declining temperature) with height given by -g/c, a constant rate, where g is the acceleration due to gravity and c is the specific heat. Note [especially you who would claim to be competent physicists] that this is entirely independent of the presence of any IR absorption by gases in the atmosphere. The available heat energy must be distributed in accordance with that constant lapse rate, and IR radiation is just one pathway for the heat to be distributed. Thus, IR absorption and emission in the atmosphere can only enable more efficient (faster) heat transport through the atmosphere, they cannot trap heat, or slow it down."
Less than 2 weeks after arriving at that simple understanding, I found the definitive evidence that disproves the greenhouse effect of increasing temperature with increasing atmospheric carbon dioxide (see here).
And I do not call it the "dry adiabatic lapse rate" either--first, of course, because that would be 9.8 K/km, while the actuality is 6.5 K/km. More importantly, simple probability considerations indicate that the difference between those two numbers is probably NOT due to the presence of water vapor, but to some other effect that increases the effective number of internal degrees of freedom of the typical air molecule from 7 (for a diatomic ideal gas) to the actual 10.5 (that gives the 6.5 K/km number)--in other words, a fairly precise, 50% increase in the effective degrees of freedom that only a highly unlikely constant proportion of atmospheric water vapor could produce, so something else must be providing that precise 50% increase.
Finally, I refer to the tropospheric lapse rate as the "hydrostatic lapse rate", because the hydrostatic condition of the atmosphere is all that is needed to produce it (that is how the Standard Atmosphere model derives it), and to deny the isothermal atmosphere.
Hi Claes,
SvaraRaderaAs you may know, we have an ongoing investigation of this issue on the talkshop. Our Loschmidt thread started about a year ago. Relevant posts can be found with this search:
http://tallbloke.wordpress.com/?s=loschmidt
There were some excellent contributions to the thread from some knowlegable contributors.
Within the last few days, I have been communicating with a contributor who has sent me experimental results supporting Loschmidt. I will be publishing these soon.
Thanks for your analysis, which is very economical. The conduction co-efficient for air is very low, hence cavity wall insulation. Regarding the column becoming isothermal: we find experimentally that the opposite is the case. When the test rig is inverted, the gradient passes through zero and reforms again. Then it remains constant, even when the gradient outside the column runs the opposite way. Graeff found the same thing. It's very curious and we are racking our brains trying to find something wrong with our test setup.
The first law of thermodynamics used by you works well when the gas is at rest or it moves with no significant changes in the height of its center of gravity, otherwise you have to take into account the potential energy of gravity, that is, generally c_vdT + gdz + pdv = dQ
SvaraRaderaIn the case of adiabatic transformation (pdv = RdT) and without external work done on the gas, the first law of thermodynamics becomes c_pdT + gdz = 0, or if you prefer, dT = - (g/c_p)dz. Then, the lapse rate is due to adiabatic upwelling of the gas without external action.
You can run your experiment in two steps. First you raise the center of gravity to its final position doing a work that equals the increase of potential energy, then you rotate the cylinder whose center of gravity doesn’t move.
So if you have gdz = 0 you will have also c_pdT = 0. Boltzmann and Maxwell are perfectly right.
Michael
Harry, don't get overheated on this issue. Loschmidt and Graeff are not necessary to overturn the GGH, it's like shooting a fly with a bazooka, this discussion is purely academical as far as a I can see.
SvaraRaderaThe problem many people seem to have is to realize that the total energy density cannot possibly be uniform in a finte atmosphere put in an infinite space, hence there must be a gradual decline in density which overturns the simple derivations.
A question that you all might want to answer: Why is there a stratosphere?
The separate but related question of the lapse rate in a planetary atmosphere is clear. Energy passing through the system will cause there to be a higher temperature at the base of the atmosphere.
SvaraRaderaGravity acts on atmospheric mass to increase pressure towards the base of the column. This also increases density, and therefore heat capacity. the greater density also means photons are more likely to hit a molecule rather than pass straight through.
A couple of questions:
SvaraRadera1) If gravity sets up a lapse rate in air why doesn't it do it in water? If there is a lapse rate in the ocean its negative and caused by surface solar heating.
2) What would happen if we built a tall cylinder, filled with water surrounded by a dry gas in a gravitational field? Would the dry gas have a lapse rate? Would the column of water not have a lapse rate? If so, would the resulting temperature difference at various heights mean that a perpetual motion machine of the second kind could be constructed?
Water is almost incompressible so heating by compression may not be operational. Erecting columns of water or air involves work so hopes to produce energy this way are probably not realistic.
SvaraRaderaBut the energy isn't lost in the column. Its still there. The big objection to Loschmidt's idea is that it implies the possibility free conversion of heat into work contrary to the 2nd law of thermodynamics. Loschmidt knew that. Maxwell knew that.
SvaraRaderaDo those who have recently taken up his argument again have an explanation of why that might be possible.
"Loschmidt's idea ... implies the possibility [of] free conversion of heat into work contrary to the 2nd law of thermodynamics."
RaderaActually it doesn't. The column is isoenergetic but not isothermal. However you cannot extract work from it.
The thought model often given to argue against this imagines connecting a metal conductor between the top and bottom of a sealed column of air thus setting up a PMM2K. Of course this is a nonsense.
But the reason that this is a nonsense is NOT because Loschmidt was wrong. It is because his principal is not being applied consistently.
In the thought model above, the metal conductor is part of the system.
Since cp (metal) >> cp(air) we find that cp(metal + air) >> cp(air) and ~ cp(metal).
When we now solve dT/dx= - g/cp we find a temperature gradient of close to zero. If you have an ideal conductor cp = ∞ then temperature gradient = 0 and the column becomes isothermal.
For real air and a real metal there will still be a small temperature gradient in both the metal and the air columns.
The system will still be in isoenergetic thermodynamic equilibrium. But not quite isothermal.
Note: Loschmidt isoenergetic principal also applies in the metal. You can only construct a PMM2K if you wrongly assume it does not.
Hence if you consistently apply Lochsmidt’s principal this does not break the 2nd Law.
" Energy passing through the system will cause there to be a higher temperature at the base of the atmosphere."
SvaraRaderaLets just think about this for a minute. Yes Solar energy is absorbed by the surface and warms the base of the atmosphere. Warm air rises, as its less dense, and transfers its energy to the upper reaches of the troposphere. From there it is radiated out into space, the air cools and falls back to the surface.
So what would happen if there were no GH effect and energy wasn't transmitted into space from the upper troposphere? The upper reaches of the troposphere , if indeed there were anything which could be called a troposphere, would have to be warmer than they are currently because there is nowhere for the heat to go.
The analogy is electric current in a wire. Normally we think that a voltage difference generates a current, but it's equally valid to say that a voltage difference can be created by a flowing current. Removing the GHE is like creating an open circuit in the wire. The current in the wire has nowhere to go and so falls to zero, meaning that the voltage difference falls to zero too.
So if, in our thought experiment, we remove the GHE, the convective heat also will have nowhere to go and the so, as the heat flux falls to zero, the temperature difference between upper and lower layers falls to zero too.
The question concerns the impact of CO2, not water vapor and clouds.
SvaraRaderaThere is more on this in the comment below and the next two after it.
SvaraRaderahttp://wattsupwiththat.com/2014/02/06/satellites-show-no-global-warming-for-17-years-5-months/#comment-1565032
You say "Of course, in planetary atmospheres external heat forcing from insolation is present."
SvaraRaderaBut on Uranus the very small amount of insolation is virtually all converted to thermal energy in the methane layer neat TOA. There is no evidence of internal energy generation, and so the whole 350Km high troposphere below that methane layer is neither receiving or emitting any significant thermal energy or radiation. So one would expect thermodynamic equilibrium to have evolved with a state of maximum entropy, or at least something very close to such. Claes thinks it would thus be isothermal, but in fact the Uranus troposphere exhibits an autonomous gravitationally induced temperature gradient very close to the -g/Cp value.
Cliaes and others
SvaraRaderaThe "lapse rate" does not require upward convection from a surface heated by the Sun's radiation. There is no such thing happening at the base of the nominal Uranus troposphere where it's hotter than Earth and the thermal gradient in the troposphere is about 95% of the -g/Cp value. These gradients evolve spontaneously at the molecular level, as I have been saying since mid-2012, even before Teofilo's book was published in October 2012, though I have just learnt of it.
The gravito-thermal effect can be verified by using Kinetic Theory in conjunction with the modern entropy statement of the Second Law of Thermodynamics, because the state of maximum entropy that evolves must have no unbalanced energy potentials, and so must be isentropic. This is explained in my new book “Why it’s not carbon dioxide after all” available on Amazon late April 2014.
It is not the energy in the oceans which controls climate just because there’s far more energy there than in the atmosphere.
Valid physics tells us it’s the other way around. It is the atmosphere (all the troposphere in particular) that autonomously comes into radiative balance with incident solar radiation, because the whole Earth+atmosphere system is what acts similar to a blackbody – not the surface, which is mostly transparent wherever there’s water.
The thermal gradient (aka lapse rate) evolves spontaneously due to gravity acting at the molecular level, and so the whole thermal profile in the troposphere is pre-determined.
Now, it doesn’t matter that the atmosphere holds far less thermal energy than the ocean. All that matters is what happens when molecules at the interface of the air and water collide. That “evens out” the temperatures and it is (eventually) thermal energy absorbed in the atmosphere that “creeps” up the (sloping) thermal plane and into the ocean. Of course the Sun adds some energy to the oceans, but its radiation passes almost entirely through the first 1cm of the surface and so its radiation is not determining the surface temperature – the troposphere is doing that by non-radiative diffusion and conduction.
Similarly, the Sun is not affecting the Venus surface temperature much with its direct radiation that is barely 20W/m^2, but that surface is over 730K. So exactly the same happens enabling energy to get into the Venus surface (by diffusion and downward convection) and this non-radiative process causes its temperature to rise during its 4-month-long daytime.
Planetary atmospheric, surface and even sub-surface temperatures are not controlled primarily by so-called greenhouse radiative forcing. That is why it’s not carbon dioxide after all.
In the 2004 paper (by Verkley et al) "On Maximum Entropy Profiles" here, they assert that ...
SvaraRadera"convective turbulent motions are now taken into account, albeit implicitly. Their role is to mix the potential temperature field, to strive to homogenize it."
This is not necessary, as there is no reasonable evidence of such convective turbulence existing on some other planets, notably Uranus. Instead it is the actual movement of molecules between collisions which provides the random mixing they claim is requiring advection. (They are not even precise in their terminology, because "convection" can include diffusion.)
They deduce in fact two conclusions using different constraints. However the constraint that leads to their deduction of isothermal conditions is not appropriate. It involves assuming constant enthalpy and this implies that there is a compensating increase in mean molecular total energy that is offset by the reduction in density at higher altitudes. This means that the molecules would be retaining equal kinetic energy, whilst gaining gravitational potential energy, that being offset by the reduction in total numbers so that total enthalpy remains constant. There is no justification for this assumption and the constraint is not a reality.
Furthermore, they introduce "constancy of the integrated potential temperature as a single additional constraint" and then they admit "but this choice is of course open for debate." Well, of course it is open for debate because there is no logic supporting it. What they are doing is trying to find a reason for the wet lapse rate being less than the dry one. They know that isentropic conditions lead to the dry rate (-g/Cp) but what they don't realise is what I have explained in my book about the temperature levelling effect of inter-molecular radiation.
As I have said all along, the empirical evidence that water vapour cools rather than warms supports the fact that the gravito-thermal effect produces the dry gradient which is then reduced in magnitude by the inter-molecular radiation, not primarily the release of latent heat.
All in all, this is a very wishy-washy paper. Whilst their computations are OK, they do not engage in any detailed discussion or reasoning as to what would be the correct constraints. It would have been appropriate to start by considering a sealed perfectly insulated cylinder of ideal non-radiating gas. If they had done this there would have been no ambiguity about the constraints or any need to discuss advection. This it the approach I have taken in my papers and the book. Once we accept that the gravito-thermal gradient evolves spontaneously at the molecular level without any need for advection, then it is not hard to extend the concept to a troposphere which has a propensity to approach such a thermal gradient, modified by inter-molecular radiation.
The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems always evolve toward thermodynamic equilibrium—the state with the maximum possible entropy.
SvaraRaderaAn isothermal profile in a gravitational field is not isentropic, for the simple reason that, firstly you are assuming all molecules have the same kinetic energy, but secondly, we know the ones at the top have more gravitational potential energy.
So, consider the following thought experiment, starting with ...
Molecules at top: More PE + equal KE
Molecules at bottom: Less PE + equal KE
In such a situation you have an unbalanced energy potential because the molecules at the top have more energy than those at the bottom. Hence you do not have the state of maximum entropy, because work can be done.
Let's consider an extremely simple case of two molecules (A & B) in an upper layer and two (C & D) in a lower layer. We will assume KE = 20 initially and give PE values such that the difference in PE is 4 units ...
At top: A (PE=14 + KE=20) B (PE=14 + KE=20)
At bottom: C (PE=10 + KE=20) D (PE=10 + KE=20)
Now suppose A collides with C. In free flight it loses 4 units of PE and gains 4 units of KE. When it collides with C it has 24 units of KE which is then shared with C so they both have 22 units of KE.
Now suppose D collides with B. In free flight it loses 4 units of KE and gains 4 units of PE. When it collides with B it has 16 units of KE which is then shared with B so they both have 18 units of KE.
So we now have
At top: B (PE=14 + KE=18) D (PE=14 + KE=18)
At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)
So we have a temperature gradient because mean KE at top is now 18 and mean KE at bottom is now 22, a difference of 4.
Note also that now we have a state of maximum entropy and no unbalanced energy potentials. You can keep on imagining collisions, but they will all maintain KE=18 at top and KE=22 at bottom. Voila! We have thermodynamic equilibrium.
But, now suppose the top ones absorb new solar energy (at the top of the Venus atmosphere) and they now have KE=20. They are still cooler than the bottom ones, so what will happen now that the previous equilibrium has been disturbed?
Consider two more collisions like the first.
We start with
At top: B (PE=14 + KE=20) D (PE=14 + KE=20)
At bottom: A (PE=10 + KE=22) C (PE=10 + KE=22)
If B collides with A it has 24 units of KE just before the collision, but then after sharing they each have 23 units. Similarly, if C collides with D they each end up with 19 units of KE. So, now we have a new equilibrium:
At top: C (PE=14 + KE=19) D (PE=14 + KE=19)
At bottom: A (PE=10 + KE=23) C (PE=10 + KE=23)
Note that the original gradient (with a difference of 4 in KE) has been re-established as expected, and some thermal energy has transferred from a cooler region (KE=20) to a warmer region that was KE=22 and is now KE=23. The additional 2 units of KE added at the top are now shared as an extra 1 unit on each level, with no energy gain or loss.
That represents the process of downward diffusion of KE to warmer regions which I call "heat creep" as it is a slow process that happens in which thermal energy "creeps" slowly up the sloping thermal profile. It happens in all tropospheres, explaining how energy gets into the Venus surface, and explaining how the Earth's troposphere "supports" surface temperatures and slows cooling at night.
See also: http://clivebest.com/blog/?p=4101
There is discussion now on Lucia's blackboard where I have just posted the following comment ...
SvaraRaderaI have produced the proof, but there is over 20 pages of it in my book “Why it’s not carbon dioxide after all” and the production process will still take until late April, even though the text was finalised well over a month ago.
Your discussion of the radiating height is countered in the book. All the necessary calculations are therein, and there is plenty of empirical data both from Earth and other planets which all gels with the hypothesis.
It’s not hard to follow the four molecule explanation above. In the book there are also diagrams that may help understanding.
I’m not going to argue over such clear cut issues as to what the Second Law says. No modern version says anything about heat only transferring from hot to cold. The four molecule thought experiment above shows why things are different in a gravitational field, but you must remember that only meticulous experiments like the 800 done by Roderich Graeff will demonstrate the small temperature differences in a lab.
Once you understand the concept of “heat creep” (downward diffusion against the temperature gradient) then you find you can answer the four questions posed above. Otherwise you can’t.
And when you understand how the energy in the lower troposphere “supports” the surface temperatures, then you will see the light and realise carbon dioxide just extends the warmth of the day maybe by a few seconds, but actually lowers very slightly the supporting temperature – and that’s what matters, as is so obvious on Venus which, by the way, is quite a bit cooler because of all the carbon dioxide.
There never will be evidence of carbon dioxide or water vapour warming, because each cools. On Venus, carbon dioxide leads to considerably lower supported surface temperatures than would be the case with an atmosphere of less-radiating gases like hydrogen and helium.
SvaraRaderaAny skeptic who still thinks carbon dioxide is having any effect at all is a warmist in my view. There can be only one truth. Those denying the truth that these gases actually cool, as is blatantly obvious in temperature data (as far as water vapour is concerned) is a denier of the truth.
The truth that nearly all are denying, lukes or warmists, lies in a whole new paradigm based on the now-proven gravito-thermal effect.
This retired physics educator puts it succinctly in summarising it all after reading the text of my book
Essential reading for an understanding of the basic physical processes which control planetary temperatures. Doug Cotton shows how simple thermodynamic physics implies that the gravitational field of a planet will establish a thermal gradient in its atmosphere. The thermal gradient, a basic property of a planet, can be used to determine the temperatures of its atmosphere, surface and sub-surface regions. The interesting concept of “heat creep” applied to diagrams of the thermal gradient is used to explain the effect of solar radiation on the temperature of a planet. The thermal gradient shows that the observed temperatures of the Earth are determined by natural processes and not by back radiation warming from greenhouse gases. Evidence is presented to show that greenhouse gases cool the Earth and do not warm it.
John Turner B.Sc.;Dip.Ed.;M.Ed.(Hons);Grad.Dip.Ed.Studies (retired physics educator)
Below is a comment I have just posted on Lucia's Blackboard in response to a common thought experiment attempting to disprove the existence of the gravito-thermal effect that is obvious in all planetary tropospheres.
SvaraRaderaThe "argument has been put to me several times and is obviously yet another attempt among climatologists to rubbish what is of course a very threatening postulate, because it smashes the greenhouse.
The argument ... does not display a correct comprehension of Kinetic Theory, or indeed the manner in which molecules move and collide.
If a perfectly isentropic state were to evolve then all molecules in any given horizontal plane would have equal kinetic energy, and of course equal potential energy, just as after the first two collisions in the 4 molecule thought experiment above.
Now, the direction in which a molecule “takes off” in its next free path motion just after a collision is random – rather like what happens with snooker balls.
So two molecules with equal KE set out in different directions after the collision, but there is no requirement that they must have more KE to go upwards. They don’t travel far anyway. It’s not as if any one molecule goes up a matter of several cm before colliding with another, for example. In fact, they nearly all travel in a direction that is not straight up or down.
At thermodynamic equilibrium (as you can see in the 4 molecule experiment) when any molecule has an upward component in its direction, it loses KE that is exactly the amount of energy represented by the difference in gravitational potential energy between the height of the molecule it last collided with and that of the next molecule. With the thermal gradient in place, the next molecule it strikes will have KE that is less than the one it last struck, and its own KE will have been reduced to exactly the same KE that the next molecule already has.
So, at thermodynamic equilibrium all collisions involve molecules which had identical KE before the collision, and so they exit the collision process still having the same KE which is the mean KE for all molecules in the horizontal plane where the collision occurred.
Now, for a small height difference, H in a “closed system” where g is the acceleration due to gravity, the loss in PE for a small ensemble of mass M moving downwards will thus be the product M.g.H because a force Mg moves the gas a distance H. But there will be a corresponding gain in KE and that will be equal to the energy required to warm the gas by a small temperature difference, T. This energy can be calculated using the specific heat Cp and this calculation yields the product M.Cp.T. Bearing in mind that there was a PE loss and a KE gain, we thus have …
M.Cp.T = – M.g.H
T/H = -g/Cp
But T/H is the temperature gradient, which is thus the quotient -g/Cp. This is the so-called “dry adiabatic lapse rate” and we don’t need to bring pressure or density into the calculation.
This now explains precisely why there is no (warming) sensitivity to carbon dioxide, because the greenhouse radiative forcing conjecture fails to explain reality. Planetary temperatures are determined primarily by the Loschmidt gravito-thermal effect, not by radiative forcing.
SvaraRaderaWe start with the second law of thermodynamics which states that "the entropy of an isolated system never decreases, because isolated systems always evolve toward thermodynamic equilibrium— a state depending on the maximum entropy."
To think of entropy as a “degree of randomness” can often lead to misunderstandings. The main concept is that isolated systems progress towards thermodynamic equilibrium, that being the state wherein entropy is maximised within the constraints of the system of course.
It now makes sense when we note that entropy can be described as “a measure of progressing towards thermodynamic equilibrium.” This way we have no ambiguity or conflict between the Second Law and the concept of entropy.
Note also that thermodynamic equilibrium is a state which has “no unbalanced potentials (or driving forces), within the system” It also embraces thermal equilibrium and people should note that thermal equilibrium does not imply isothermal conditions, just no transfer of kinetic energy across a boundary.
But, if we start with isothermal rows of molecules (say, 68nm apart in altitude) we see the top row losing kinetic energy and the bottom row gaining kinetic energy as molecules go up and down across the boundary between the rows, because the sum of kinetic energy and gravitational potential energy is kept constant as they move, and then, when they collide, the total kinetic energy of the two molecules is shared equally between them. (See my four molecule thought experiment in a comment above.).
So the isothermal state was not in thermal equilibrium, and thus not the state of thermodynamic equilibrium. The Second Law implies that will change. It only stops changing when, in the absence of inter-molecular radiation, the difference in gravitational potential energy between the rows equals the difference in kinetic energy. Then, and only then, do we have thermodynamic equilibrium. Not surprisingly, entropy is homogeneous and so there are no unbalanced energy potentials that would lead to further increases in entropy.
Yes, you must include gravitational potential energy in all this, because thermodynamic equilibrium also includes mechanical equilibrium, and that means no net movements of more molecules going downwards than upwards. Obviously the external force of gravity does affect the kinetic energy distribution, leading to the gravito-thermal gradient which I consider thus proven by induction from the four molecule thought experiment.
Furthermore, it is confirmed by data from throughout the Solar System.
Further experimental proof of the Loschmidt gravito-thermal effect can be easily seen in a Ranque-Hilsch vortex tube wherein a force far greater than gravity separates a gas into measurably hotter and colder streams as it redistributes kinetic energy, just as happens in a planet's troposphere due to the force of gravity.
SvaraRaderaJust remember there's going to be a genuine $5,000 reward for the first to come up with proof I'm wrong and proof IPCC are right about water vapour - see last paragraph..
SvaraRaderaIn a horizontal plane you can observe diffusion of kinetic energy in your home. Just run a heater on one side of a room, turn it off or even remove it quickly from the room, and you will temporarily have measureably warmer air on one side of the room. Molecules then keep on colliding and as they do, kinetic energy is shared. Statistical mechanics tells us that temperature (that is, mean kinetic energy per molecule) will even out across the room assuming it's well insulated.
Suppose now that the room has double glazed windows and it's cooler outside. Which is more effective at insulating the room?
(a) A window with dry air or even argon
(b) A window with moist air - say 4% water vapour or water gas
(c) A window full of carbon dioxide only, like the Venus atmosphere?
The answer is the dry air or argon, as is well known in the construction industry. Why? Because radiating "pollutants" like water gas and carbon dioxide send the energy across the gap (and up through the troposphere) with inter-molecular radiation. Such radiation only ever transfers thermal energy from warmer to cooler regions. Otherwise what happens is as described in "Radiated Energy and the Second Law of Thermodynamics."
Why then does the thermal gradient reduce in magnitude because of the inter-molecular radiation between carbon dioxide molecules in the Venus atmosphere, or between a few methane molecules in the Uranus troposphere or between water vapour molecules in Earth's troposphere and Earth's outer 9Km of its crust?
All these thermal gradients (aka lapse rates) are less steep than they would have been in dry air or (nearly) non-radiating gases. Gravity would have induced a steeper -g/Cp gradient.
The thermal gradient in the Uranus troposphere does not level out (despite no solar radiation or any surface) because to do so would violate the Second Law of Thermodynamics. It seems most of you don't understand why, but the reason is that entropy would decrease. If somehow a state were to evolve with more gravitational potential energy per molecule at the top, but no compensating reduction in kinetic energy per molecule (ie temperature) then there would be unbalanced energy potentials at the top, so work could be done and thus entropy would not have been at a maximum. The four molecule experiment demonstrates this and how it happens at the molecular level.
The vortex tube demonstrates it, and kinetic energy is re-distributed such that the inner tube gets far colder than the air that was pumped in. So you can't blame friction for heating the outer tube. Nor does pressure alter temperature, because pressure is proportional to the product of temperature and density: temperature is an independent variable and only varies when mean kinetic energy per molecule varies.
Finally, none of you can explain how the Venus surface actually rises in temperature from 732K to 737K during its four-month-long day, unless you start by understanding that the thermal gradient is the state of thermodynamic equilibrium. Then you need to understand the mechanism of "heat creep" explained in the second part of the four molecule experiment.
There will be a $5,000 reward for the first to prove me wrong with conditions explained in public advertisements and on all of a dozen or so of my websites. To win the award you will also have to show empirical evidence of the IPCC postulate that the sensitivity to water vapour is of the order of 10 degrees of warming for every 1% increase in the Earth's troposphere.
Just remember there's going to be a genuine $5,000 reward for the first to come up with proof I'm wrong and proof IPCC are right about water vapour - see last paragraph..
SvaraRaderaIn a horizontal plane you can observe diffusion of kinetic energy in your home. Just run a heater on one side of a room, turn it off or even remove it quickly from the room, and you will temporarily have measureably warmer air on one side of the room. Molecules then keep on colliding and as they do, kinetic energy is shared. Statistical mechanics tells us that temperature (that is, mean kinetic energy per molecule) will even out across the room assuming it's well insulated.
Suppose now that the room has double glazed windows and it's cooler outside. Which is more effective at insulating the room?
(a) A window with dry air or even argon
(b) A window with moist air - say 4% water vapour or water gas
(c) A window full of carbon dioxide only, like the Venus atmosphere?
The answer is the dry air or argon, as is well known in the construction industry. Why? Because radiating "pollutants" like water gas and carbon dioxide send the energy across the gap (and up through the troposphere) with inter-molecular radiation. Such radiation only ever transfers thermal energy from warmer to cooler regions. Otherwise what happens is as described in "Radiated Energy and the Second Law of Thermodynamics."
Why then does the thermal gradient reduce in magnitude because of the inter-molecular radiation between carbon dioxide molecules in the Venus atmosphere, or between a few methane molecules in the Uranus troposphere or between water vapour molecules in Earth's troposphere and Earth's outer 9Km of its crust?
All these thermal gradients (aka lapse rates) are less steep than they would have been in dry air or (nearly) non-radiating gases. Gravity would have induced a steeper -g/Cp gradient.
The thermal gradient in the Uranus troposphere does not level out (despite no solar radiation or any surface) because to do so would violate the Second Law of Thermodynamics. It seems most of you don't understand why, but the reason is that entropy would decrease. If somehow a state were to evolve with more gravitational potential energy per molecule at the top, but no compensating reduction in kinetic energy per molecule (ie temperature) then there would be unbalanced energy potentials at the top, so work could be done and thus entropy would not have been at a maximum. The four molecule experiment demonstrates this and how it happens at the molecular level.
The Ranque-Hilsch vortex tube demonstrates it, and kinetic energy is re-distributed such that the inner tube gets far colder than the air that was pumped in. So you can't blame friction for heating the outer tube. Nor does pressure alter temperature, because pressure is proportional to the product of temperature and density: temperature is an independent variable and only varies when mean kinetic energy per molecule varies.
Finally, none of you can explain how the Venus surface actually rises in temperature from 732K to 737K during its four-month-long day, unless you start by understanding that the thermal gradient is the state of thermodynamic equilibrium. Then you need to understand the mechanism of "heat creep" explained in the second part of the four molecule experiment.
There will be a $5,000 reward for the first to prove me wrong with conditions explained in public advertisements and on all of a dozen or so of my websites. To win the award you will also have to show empirical evidence of the IPCC postulate that the sensitivity to water vapour is of the order of 10 degrees of warming for every 1% increase in the Earth's troposphere.
Claes - the centrifugal experiment demonstrates the thermal gradient
SvaraRaderaRead about the Ranque-Hilsch Vortex tube and note that it generates a huge force of about 10^7g which, in the 1cm radius (10^-5Km), using Cp=1 gives a temperature difference of 10^7/10^5 = 100 degrees. The observed results are of this order of magnitude, which means the Loschmidt gravito-thermal effect seems the most probable explanation.
Actually I should correct those calculations. 10^7g is about 10^8 because g=9.8. Now I know that then gives 1,000 degrees and the quoted range is 250 degrees, but the factor of 4 in the difference is not unacceptable because of all the variables involved, especially the fact the g force is much less in the central tube. So we would expect that the mean g force might indeed be between 10^7 and 10^8.
SvaraRaderaThe Second Law of Thermodynamics is not a simplistic rule that heat always transfers from warmer to cooler regions if there is a temperature difference.
SvaraRaderaIn the early pre-dawn hours the lower troposphere still exhibits the expected thermal gradient, but meteorologists know that convection stops. Yes energy flow stops even though there is warmer air at lower altitudes. That is because there is thermodynamic equilibrium, and when we have thermodynamic equilibrium - well, you can look up in Wikipedia all the conditions and things that happen.
The real Second Law of Thermodynamics takes quite a bit of understanding and many hours, maybe years of study. You guys have absolutely no understanding of it, as I can detect from my decades of helping students understand physics.
To understand it you have to really understand entropy for starters. Then you have to really understand thermodynamic equilibrium and all the other states, such as mechanical equilibrium, thermal equilibrium etc which the Second Law embraces. That is why, for example, you cannot disregard gravity and gravitational potential energy when determining the state of maximum entropy attainable by an isolated system. The gravito-thermal effect is a reality.
If you want to stay in the mid-19th century when much of this physics was not widely understood, and if you want to imagine, for example, that radiative heat transfer does not obey the Second Law, then all I can say is that you must live in a strange and isolated planet, because you sure can't answer my questions about other planets with your climatology paradigm.
When you truly understand the Second Law of Thermodynamics then, and only then, will you start to understand how it explains the so-called lapse rate and how the pre-determined thermal profile supports surface temperatures everywhere, not back radiation from a cooler atmosphere. Thus you will understand why it's not carbon dioxide after all.
Claes and all readers: this is important.
SvaraRaderaSkeptical Science team member Neal J King writes on Lucia's Blackboard, referring to thermodynamic equilibrium: "a transfer of energy δE between two sub-components, j = 1 and j = 2, will change neither E_total nor, to 1st order, S_total"
Yes, and that is exactly what happens when there is a thermal gradient such that the difference in mean kinetic energy per molecule (temperature) exactly matches the negative of the difference in mean gravitational potential energy per molecule.
You can see this in the second stage of the four molecule experiment: when thermodynamic equilibrium is attained we have homogeneous entropy (which must take PE into account) and every collision involves molecules with equal KE, and so KE for the system does not change, but is different per molecule at different altitudes. Similar happens in diffusion in a horizontal plane - KE of all molecules approaches homogeneity. But in a vertical plane you have to remember that KE changes because PE changes whenever there is a non-zero vertical component in the free path vector between collisions.
The gravito-thermal effect is blatantly obvious when convection stops in the early pre-dawn hours. It is then that the pre-determined thermal profile has a "supporting temperature" at the base of the troposphere on any planet. That is what explains all the observations on all planets with surfaces, and even planets without surfaces. Temperatures are set based on radiative balance and the gravito-thermal gradient.
The probability of these thermal gradients being so close to the -g/Cp value on all planets with significant tropospheres just because of some assumed warming by the Sun (whose radiation barely reaches some planetary surfaces) is absolutely infinitesimal. The evidence for the gravito-thermal gradient is blatantly obvious everywhere, as is the theory behind it.
And as for radiation from carbon dioxide supposedly helping the Sun to attain greater maximum temperatures each day (despite the Second Law) or even just slowing radiative cooling - so what? Oxygen and nitrogen slow non-radiative cooling and outnumber carbon dioxide 2,500:1. Radiation from carbon dioxide (with its limited frequencies) is like a picket fence (with most of its pickets missing) standing up against a torrent of full spectrum radiation from the surface. The mean temperature of carbon dioxide molecules in Earth's troposphere is far colder than the mean temperature of oxygen and nitrogen molecules colliding at the boundary with surface molecules. Rates of cooling depend on temperature gaps, so think!
But arguing with lukes and warmists is like playing chess with a pidgeon. No matter how good a player I am, the pigeon knocks over the pieces, craps on the board and struts around looking victorious.
PROOF of EXISTENCE of the GRAVITO-THERMAL EFFECT
SvaraRadera(1) The second law of thermodynamics states that "the entropy of an isolated system never decreases, because isolated systems always evolve toward thermodynamic equilibrium— a state depending on the maximum entropy."
(2) "In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. Equilibrium means a state of balance. In a state of thermodynamic equilibrium, there are no net flows of matter or of energy, no phase changes, and no unbalanced potentials (or driving forces), within the system. A system that is in thermodynamic equilibrium experiences no changes when it is isolated from its surroundings."
(3) When, in the absence of phase change, chemical reaction or inter-molecular radiation, a gas has reached thermodynamic equilibrium, then there will be no net change in the distribution of energy on a macro scale.
(4) In such circumstances described in (3) for every molecular movement between collisions, any change in gravitational potential energy must be countered by an opposite change in kinetic energy.
(5) If (2) applies and noting (4) it follows that when any given molecule is about to collide with another, its own kinetic energy must be equal to that of the target molecule so that no net change occurs in the collision.
(6) Hence, for any pair of molecules at different heights (or altitudes) the difference in gravitational potential energy must be offset by an equal and opposite difference in kinetic energy, thus maintaining a homogeneous sum (KE+PE) for all molecules.
(7) Thus, because temperature is a function only of the mean KE per molecule, and because PE varies so must KE vary, causing a thermal gradient throughout the whole system,
There can be no correlation found between temperature data and carbon dioxide, because it cools only by about 0.1 degree. You need to come to grips with the new 21st century paradigm shift in climate science based upon the gravito-thermal effect.
SvaraRaderaThis is how absurd the old 20th century paradigm of greenhouse radiative forcing gets. They claim that you can work out Earth's surface temperature by adding together the radiative flux from both the Sun and the colder atmosphere, and then bunging this total value into the Stefan-Boltzmann equation and out pops your answer 287K or 288K. Well it might well do if you fiddle the back radiation and then use the emissivity value instead of the absorptivity.
But there's absolutely no physics to support the calculations. When you consider that about 70% of the surface is a thin transparent water layer, it is obvious that the solar radiation which mostly (like over 99%) passes through this layer into the thermocline is not what is determining the temperature of that thin surface layer. In fact the mean temperature of the thermocline is obviously less, and the mean temperature of all the ocean water is less again.
Oh, and the back radiation doesn't even enter the surface layer - it just raises electrons between quantum energy states momentarily, and then those electrons immediately emit another photon which climatologists think is energy coming from the kinetic energy in the surface molecules, but it's only electro-magnetic energy from the back radiation being thrown back in their red faces.
SUMMARY
SvaraRaderaIn an adiabatic process in a sealed and perfectly insulated vertical cylinder of a solid, liquid or gas a thermal gradient evolves in accord with the process described in statements of the Second Law of Thermodynamics.
This fact may be used to deduce that such will also occur in calm conditions in a planet's troposphere if no new energy were being absorbed, such as is close to the case in calm conditions in the early pre-dawn hours, when surface cooling and upward advection almost stops. In such as situation we can observe that there is indeed a thermal gradient, but there is no heat transfer from the lower warmer regions to the cooler regions above, for the simple reason that there is already a state of thermodynamic equilibrium.
Molecules move in random directions after each collision, and the direction is not significantly dependent upon the kinetic energy in the molecule. So the calculation of the thermal gradient has nothing to do with pressure or density or rising packets of air. There is no such thing as a moving packet of air in adiabatic conditions anyway, because the probability of trillions of molecules all moving in the same direction is absolutely infinitesimal in the absence of wind or forced advection caused by an external energy source like a fan.
Temperature is the independent variable and only changes if mean molecular kinetic energy changes. Gravity sets up non-zero gradients in density and temperature. Pressure is merely the end result because pressure is proportional to the product of density and temperature.
My study showing water vapour cools is not hard to replicate. To prove me wrong you would have to produce a similar study proving water vapour warms by about 10 degrees for each 1%, as is in effect claimed by GH advocates.
SvaraRaderaThe Ranque-Hilsch vortex tube provides evidence of the gravito-thermal effect. You would need to provide contrary empirical evidence.
You would also need to produce a valid (but different) explanation as to how the necessary thermal energy gets into the Venus surface in order to raise its temperature by 5 degrees during its sunlit hours.
BigWaveDave considers the gravito-thermal effect (seen in the vortex tube) worth your time thinking about …
“Because the import of the consequence of the radial temperature gradient created by pressurizing a spherical body of gas by gravity, from the inside only, is that it obviates the need for concern over GHG’s. And, because this is based on long established fundamental principles that were apparently forgotten or never learned by many PhD’s, it is not something that can be left as an acceptable disagreement.”
The greenhouse conjecture would violate the laws of physics. It is totally wrong.
The Ranque-Hilsch vortex tube confirms the existence of the Loschmidt temperature gradient in a force field,
SvaraRaderaNo, the isothermal state cannot exist as an equilibrium state because it is not the state of maximum entropy. A new heat source disturbs the equilibrium and so thermal energy from that new source disperses in all accessible directions (including downwards) until a new state of thermodynamic equilibrium (with its associated temperature gradient) is established at a higher overall temperature but the same temperature gradient.
SvaraRaderaThe Ranque Hilsch vortex tube is the best "experimental test" of the fact that molecular kinetic energy is redistributed in a force field, forming a temperature gradient.
SvaraRaderaBecause the temperature gradient in a planet's troposphere is the state of thermodynamic equilibrium which the Second Law of Thermodynamics says will evolve, the planet’s supported surface temperature is autonomously warmer than its mean radiating temperature, so warm in fact on Earth that we need radiating gases (mostly water vapour) to reduce the gradient and thus cool the surface from a mean of about 300K to about 288K, this being confirmed by empirical evidence (as in the study in my book) which confirms with statistical significance that water vapour cools rather than warms, all these facts thus debunking the greenhouse conjecture.
A review of the new book "CLIMATE CHANGE THE FACTS 2014" by about 24 authors - available here.
SvaraRaderaThe best and most relevant chapter in this new book is that by William Soon, namely Chapter 4 "Sun Shunned" in which he discusses things such as the eccentricity of the Sun's orbit that I have also pointed out as the principal regulator of glacial periods.
The rest of the chapters on the "science" do not discuss the valid physics which is really what does determine Earth's surface temperatures. Instead the "lukes" all reiterate the false claim that carbon dioxide causes significant warming of the surface by radiative forcing. Nowhere is the assumed process of forcing actually discussed. We just get the usual false paradigm that carbon dioxide traps outward radiation and thus supposedly makes the surface warmer.
Carbon dioxide does not trap thermal energy. It disposes of what it absorbs either by subsequent radiation or by sensible heat transfer (via molecular collisions) to other air molecules which outnumber it by 2,500 to 1. It also helps nitrogen and oxygen cool through such collisions, and may subsequently radiate the energy thus acquired out of the atmosphere.
All radiation between regions at different temperatures can only transfer thermal energy from the warmer region (or surface) to a cooler region. This means all heat transfer in the troposphere is generally upwards to cooler regions, with a proportion always getting through to space. There is no thermal energy transferred to a warmer surface. The energy transfer is the other way. The Sun's radiation is not helped by radiation from the atmosphere which is only sending back some of its own energy now with much lower energy photons. Radiating gases reduce the insulating effect by helping energy to escape faster, and that is why moist air in double glazed windows also reduces the insulating effect, just as does water vapor in the troposphere.
(continued)
SvaraRaderaNowhere in the book do we see the surface temperature explained correctly using Stefan Boltzmann calculations. No one ever does this, because it is an absolute stumbling block for climatologists. The mean solar flux entering the surface is only about 163W/m^2 after 52% of the solar radiation has been either absorbed or reflected by the surface, clouds or atmosphere. But such a low level of radiation would only produce a very cold -41°C. That's even colder than what the IPCC claims would be the case, namely -18°C without greenhouse gases. They deduce that by assuming that the whole troposphere would be isothermal due to convective heat transfer, including sensible heat transfers by molecular collision.
Hence all the "luke" authors fall for the trap of not actually explaining the existing surface temperature, let alone what carbon dioxide might or might not do. How could you work out the latter if you don't know your starting point? The truth is that you cannot calculate the surface temperature of any planet that has a significant atmosphere by using radiation calculations. Hence all the considerations pertaining to radiation and absorption by carbon dioxide are totally within a wrong paradigm.
That assumption by the IPCC (and thus by the "lukes" who have written this book) that the troposphere would be isothermal was rubbished in the 19th century by some physicists who understood the process described in statements of the Second Law of Thermodynamics. It is still being rubbished to this day, and even more so, now that physicists realise that the Second Law is all about entropy increasing to the point where there are no unbalanced energy potentials. In a gravitational field this state of thermodynamic equilibrium is attained when all the energy potentials involving gravitational potential energy, kinetic energy and radiative energy balance out. That is when the environmental temperature gradient is attained, and the very fact that it exists enables us to explain all planetary surface temperatures (and the required energy flows) without the slightest reference to back radiation, let alone trace gases like carbon dioxide. Only water vapor has a significant effect in lowering that gradient because of its radiating properties. It thus cools the surface, and that puts a big spanner in the works for the IPCC et al.
SvaraRaderaAN "IDEAL" AVERAGE TROPOSPHERE
It is instructive to consider an "ideal" perfectly calm (wind-less) region on Earth that is above a calm ocean at a mean latitude of 45° on March 21st when the Sun is above the Equator. We will assume there is a non-transparent layer of cloud covering the selected region and beyond and that region. The cloud is at an altitude where the temperature is the mean effective radiating temperature of 255K.
Now, the cloud layer will reflect solar radiation, and we will assume no reflection goes downwards. Hence all solar radiation can only raise the temperature of the clouds (to 255K) and regions above the clouds. The radiation can do so on its way down to the clouds and also on its way back up, because it still has the same frequency distribution and intensity after reflection. Any back radiation from above the clouds will of course not go down below the clouds, and will not raise the temperature of the clouds above 255K anyway.
Based on mean temperature data for locations at such latitudes in ocean regions I think you will find that the annual mean temperature is about 9°C as it is for Invercargill near the ocean at the southern tip of New Zealand. I seriously doubt the IPCC estimate of 14°C to 15°C.
Why is it so? Why is the surface that much warmer than the clouds when no solar radiation gets through the clouds?
Firstly, I have proved here that the environmental temperature gradient (aka lapse rate) is the state of thermodynamic equilibrium which the Second Law says will evolve.
Secondly, I have proved from the Second Law that, if that state is disturbed by the absorption of new thermal energy at the top, then downward convective heat transfer is possible.
So the ocean surface temperature is raised slightly by day by the downward convective heat transfer from the clouds and that temperature is supported long-term around the 9°C mark due to the gravitationally induced temperature gradient which enables heat transfer over the sloping thermal plane in all directions away from a new source of energy.
Heatwaves have nothing to do with carbon dioxide, because the whole concept that planetary surface temperatures are determined primarily by direct solar radiation is totally incorrect. The planet Uranus, for example, has no surface at the base of its nominal troposphere where the temperatures is about 47°C.
SvaraRaderaA study of this nominal troposphere of Uranus confirms that the temperature gradient is about 95% of the -g/Cp value mentioned below. All tropospheres have slightly less steep gradients because of the temperature-leveling effect of inter-molecular radiation between IR-active molecules. The temperature gradient (aka "lapse rate") is the state of thermodynamic equilibrium which the Second Law of Thermodynamics says will evolve autonomously as entropy approaches the maximum. At that maximum there can be no unbalanced energy potentials, and so, other forms of energy being equal, there must be a homogeneous sum of molecular gravitational potential energy and kinetic energy. Because PE varies with altitude, and because temperature is proportional to mean molecular KE only, there must be a temperature gradient, which we can calculate to be -g/Cp where Cp is the weighted mean specific heat of the gases.
Now, because the temperature gradient represents the state of thermodynamic equilibrium, any new thermal energy absorbed in the upper atmosphere from insolation will disturb the equilibrium and lead to a new state of thermodynamic equilibrium evolving with the same temperature gradient, but a higher overall temperature. This means some thermal energy moves downwards to warmer regions, not by radiation, but by convective heat transfer which, in physics, includes transfers of KE in molecular collisions and diffusion.
All this is explained in more detail in our group's website and you can read about Uranus on the 'Evidence' page therein.
What happens in the real universe is a complete paradigm shift from what climatologists think about planets cooling off and having surfaces warmed only by solar radiation. All planetary temperatures are determined from the "anchor point" in their atmosphere right down to their cores, and all temperatures en route are supported by downward diffusion and convective heat transfer from the anchor point, that being where there is radiative equilibrium with the Sun. If the Sun's radiation somehow ceased, then all planets and satellite moons would cool right down, even their cores wherein any energy generation is in reality nowhere near sufficient to maintain existing temperatures, and not necessary anyway. That's what the Second Law of Thermodynamics gives us reason to say must be the case.
https://www.researchgate.net/publication/337915638_Understanding_Josef_Loschmidt's_Gravito-_Thermal_Effect_and_thus_Why_the_Radiative_Forcing_Greenhouse_Hypothesis_is_False
SvaraRadera