# Earth’s Energy Balance

With the sun directly overhead and clear skies, earth’s surface receives about 1,000 watts per meter² shortwave radiation during mid-latitude summer.  If you could convert that into electricity with 100% efficiency, that would power ten 100 watt light bulbs at noon. During winter, that is reduced to 300 watts per meter² on a clear day at noon.  A rooftop covered with solar panels can potentially generate a lot of electricity – when conditions are optimal.

Using the AER RRTM model, I calculated the amount of longwave radiation reaching the ground during mid-latitude summer, is 349 watts per meter².  About 97% of that is due to water vapor, and 3% is due to CO2.

During mid-latitude winter, the amount of downwelling longwave radiation is 224 watts per meter² – about 89% due to water vapor and 11% due to CO2.  CO2 has more effect during winter, because there is less H2O in the atmosphere competing for the same wavelengths of longwave radiation.

During winter, the sun is relatively less important and the greenhouse effect is relatively more important.

Now consider the Antarctic winter. There is no shortwave radiation (blue) and very little H2O (red) in the atmosphere to emit longwave radiation.  Thus there is little downwelling radiation – and extremely cold temperatures.

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### 95 Responses to Earth’s Energy Balance

1. Chaeremon says:

A: because the atoms on the ground know their angle to the Sun.
Q: why would the Sun deliver less watts per meter² during winter – for the model calculation and not for your sunburn in winter snow?

2. David says:

Well because your sunburn is caused by ultra violet radiation and not the wavelengths that are in this discussion.

• Chaeremon says:

You read the description from a suncream flask, because … science?

You hold your arm before a LW heater rod, doesn’t hurt the skin like sunburn does, because … science?

What about the angle, … science?

3. Ed Bo says:

The really interesting thing about the Antarctic winter is the months-long temperature inversion (positive lapse rate), which leads to a cooling “anti-greenhouse” effect there as some of the radiation to space occurs from the higher temperatures aloft rather than from the colder surface.

4. Hivemind says:

“If …, that would power ten 100 watt light bulbs at noon.”

Except that I can’t think of a reason I would want to power any light bulbs at noon. The problem is that at midnight, when I do want to power my light bulbs, the solar panels are producing absolutely no power for some reason. I don’t know why, but am willing to study the problem for a large enough grant.

5. spike55 says:

And remember, that if there is any surface warming beyond what can be held by the gravity based pressure/temperature gradient, it is removed by convection.

That gradient and the effects of atmospheric H2O within that gradient are a strong regulator on the planet’s maximum temperatures.

6. Ed Bo says:

spike:

Care to explain how the “gravity based … temperature gradient” explains the positive lapse rate (temperature increasing with altitude) that lasts for months every winter over the entire Antarctic continent?

• spike55 says:

inversion due to very cold surface

Pressure says the surface should be far warmer than it is.

(this may be a repeat because I got a “bad gateway” error last time)

• Ed Bo says:

How warm does “pressure say[] the surface should be”?

If the “inversion [is] due to very cold surface”, why isn’t a negative lapse rate due to “very hot surface”?

• spike55 says:

OMG, Ed Bo doesn’t understand the natural pressure temperature gradient, lapse rate and convection.

I have better things to do that try and teach someone that doesn’t want to know.

• Ed Bo says:

James Clerk Maxwell demonstrated in the mid 1800s that gravity alone could not induce a temperature lapse rate, as this would lead to blatant 2nd LoT violation. (Of course, there is a gravitationally induced pressure gradient — a very different issue.)

In Feynman’s classic Lectures on Physics from the 1960s, still used widely today, he dispenses with the idea of a gravitationally induced temperature gradient in a single paragraph.

You’re only 150 years behind the times. Please do try to keep up!

• spike55 says:

OK, so there isn’t any gravity and there isn’t an induce temperature gradient CALCULATED from that gravity value in a dry atmosphere.

really !!!!

Its AMAZING that it doesn’t exist, despite all real measured observations. !

Its amazing that the GRAVITY constant is used to calculate this mythical lapse rate, that it has nothing to do with.

roflmao. !!

It requires some SOLAR input as well, bozo !!

The gravity based pressure/temperature gradient allows the surface to maintain a certain amount of energy.

What don’t you comprehend??

• Ed Bo says:

When energy is added to something at one end and removed from it at the other end, you get a temperature gradient across it. Not a difficult concept.

On the daytime side, energy is added to the atmosphere primarily from the bottom, as the atmosphere is mostly transparent to solar radiation, most of which makes it to the surface.

Energy is lost from the atmosphere primarily from the top, as the atmosphere is mostly opaque to longwave infrared radiation. These are empirical FACTS, as confirmed by countless measurements.

This is what creates the common negative lapse rate we see in the earth’s atmosphere. If this lapse rate is of greater magnitude than the adiabatic lapse rate, it is what is commonly known as an “unstable lapse rate”. When the lapse rate is unstable, convection is induced, which drives the lapse rate back toward adiabatic (-g/cp).

You get this backwards. You think that convection induces the lapse rate. No! The lapse rate (greater than adiabatic) induces convection. This is basic, introductory physics.

When the atmosphere is losing energy primarily from the bottom, as is common when the sun doesn’t shine, particularly when LWIR absorption is low (clear skies, low absolute humidity), you get a positive lapse rate.

And you haven’t even attempted to grapple with the concept that a lapse rate from gravity alone yields a gross violation of the 2nd Law of Thermodynamics. Why not????

• spike55 says:

Air rises because it expands when heated

The density decreases so it must equalise to a similar density. That is what CONVECTION is.

The Density gradient is caused by PRESSURE.

The Pressure gradient is caused by GRAVITY.

DENIAL of the measured, observed, temperature gradient which is calculated using ONLY the GRAVITY constant and the specific energy of the atmosphere.

REALLY ??????

It is

• spike55 says:

Its very simple. even little Ed should be able to comprehend this.

If the temperature at the surface is GREATER than the gravity based pressure temperature gradient can sustain, heat rises, ie CONVECTION.

If not, and the surface is being warmed, then it keeps warming until that CONVECTIVE cooling starts.

The temperature-pressure gradient, due to the effect of gravity, is the CONTROL, the REGULATOR.

Comprehend, little Ed !!

• Ed Bo says:

spike, you say: “If the temperature at the surface is GREATER than the gravity based pressure temperature gradient can sustain, heat rises, ie CONVECTION.

If not, and the surface is being warmed, then it keeps warming until that CONVECTIVE cooling starts.

The temperature-pressure gradient, due to the effect of gravity, is the CONTROL, the REGULATOR.”

That is exactly what I have been saying!!!

But the EXISTENCE of this negative lapse rate is NOT CAUSED by gravity; it is caused by the differential heating/cooling of the atmosphere due to the fact that the atmosphere is more transparent to solar than to LWIR radiation.

That was my whole reason I pointed out the positive lapse rate over Antarctica all winter.

7. Eben says:

Any substance that eagerly absorbs radiation will just as eagerly re-emit it depending on the temperature it is at and the radiation it receives, in the winter conditions at the polar region the greenhouse effect (which by the way has nothing to do with greenhouse) will not be diminished it will be completely reversed, in other words CO2 causes faster cooling , the idiotic claims about CO2 acting as a blanket never account for this.

• Squidly says:

I’m still trying to figure out how the surface can heat itself … man, this CO2 and water vapor stuff is like magic!

• spike55 says:

The air above the Antarctic is actually COLD ENOUGH for CO2 to re-emit. -80C

Over most of the world, CO2 cannot re-emit until several km altitude.

It just thermalises to the other 99,96% of the atmosphere where it is dealt with by the over-riding convective forces, which are of course controlled by the observed and measured and calculated gravity induced pressure temperature gradient.

Yes, yes, Ed…. I know the gravity induced pressure temperature gradient doesn’t exist

…. except basically everywhere in the atmosphere.

…. and the gravitation constant is never used to calculate the change in temperature at altitude in the atmosphere,

because, as we all know thanks to ed, gravity has nothing to do with it…. right !

• Ed Bo says:

spike:

Are you seriously claiming that CO2 above -80C does not emit IR???

Why do the satellites detect radiation from CO2 at far higher temperatures than that?

Why can you detect radiation from CO2 in the laboratory at room temperature?

Why do you get essentially everything completely wrong?

• spike55 says:

Oh dearie me, You do know that in the lower atmosphere the thermalisation time of energy absorbed by CO2 is several magnitudes FASTER than the re-emittance time, don’t you.?

Do you really think that the atmosphere is like a glass jar in a laboratory

WOW.

Its wacky la-la time in Eb’s mind tonight !!

Quite bizzare really

Here we have a known, calculated observed , measured, thermal lapse rate calculated PURELY from the gravitational constant and the specific energy of the atmosphere, on EVERY planet with a viable atmosphere.

and Ed DENIES its existence

Then we have a anti-physics, never measured, never observed warming myth from CO2.. and the likes of Ed get totally sucked in by it.

Wacky !!!

• Ed Bo says:

spike, now you say: “You do know that in the lower atmosphere the thermalisation time of energy absorbed by CO2 is several magnitudes FASTER than the re-emittance time, don’t you.?”

Of course, I do! But I was reacting to a very different, anc completely erroneous claim, that you made: “The air above the Antarctic is actually COLD ENOUGH for CO2 to re-emit. -80C. Over most of the world, CO2 cannot re-emit until several km altitude.”

When a particular CO2 molecule is excited by IR, it is much more likely to pass off that energy by collision than it is by emitting another IR photon. But CO2 molecules low in the atmosphere are emitting IR all the time.

Point a spectroradiometer upwards when the sky is clear. You get lots of downwelling radiation in the ~15um wavelength band, with a magnitude that shows that it is coming from temperatures present near the surface. This is experimental DISPROOF of your argument that “CO2 cannot re-emit until several km altitude.”

You apparently have this idea mixed up with the idea of how high the CO2 molecule must be before its radiation is likely to escape to space. But this is a function of density, not temperature.

And more fundamentally, you fail to comprehend my basic argument that gravity does not CAUSE a negative lapse rate (differential heating/cooling does), but it does LIMIT it because lapse rates greater than adiabatic are unstable and induce convection. And the differential heating/cooling effect is strong enough on all planetary bodies we see to induce this convection, driving the lapse rate towards the adiabatic slopes that we observe.

• spike55 says:

What is the mean free path of CO2 emission frequency in the lower atmosphere, Mr Ed…… if it actually existed. !

At 0.04% of the atmosphere, we must be literally FLOODED with this evil radiation. !!

Right ;-)

8. Squidly says:

So, let me get this straight .. the LWR (long wave radiation) comes from the surface, radiating away being absorbed by Water Vapor and CO2, then re-radiated back towards the surface again.

Tell me, how does the surface heat itself? … Why can’t I just place a mirror in front of me to stay warm?

• Ed Bo says:

squidly:

Go to a camping supply store. Lots of the clothing has reflective (i.e. mirrored) surfaces on the inside. The whole point is to keep you warm.

• spike55 says:

roflmao,

Ed thinks CO2 is a blanket….

ROFLMAO !!!!!

Looks like the village idiot has escaped again.

No, little Ed,

CO2 DOES NOT stop or slow CONVECTION.

Nor does it stop radiation escaping, just thermalises it to the rest of the atmosphere where CONVECTION talks over.

It DOES NOT cause warming.

It is NOT a reflective or any other sort of blanket.

Warming by atmospheric CO2 has never been observed or measured, anywhere.

• Ed Bo says:

spike, you say: “CO2 DOES NOT stop or slow CONVECTION.”

I never claimed that it did. You are completely unable to follow an argument.

Then you say: “Nor does it stop radiation escaping, just thermalises it to the rest of the atmosphere where CONVECTION talks over.”

So let’s break down the process into baby steps. First, the CO2 low in the atmosphere absorbs some longwave IR that otherwise would “escape” to space. (In my book that is “stop[ping] radiation escaping”.)

Then, most of this absorbed energy is thermalized to other molecules in the atmosphere, making it warmer than it otherwise would be.

If this absorption and thermalization low in the atmosphere creates a negative lapse rate larger than adiabatic, this unstable lapse rate induces convection.

Convection does not eliminate the lapse rate, but it does limit the magnitude. So high in the atmosphere, where the density is low enough that CO2 emitted IR can escape to space, it is doing so at a lower temperature, and therefore lower intensity than if surface-emitted radiation could “escape” to space.

And I repeat that CO2 is emitting IR at all altitudes; it is just that it is much more likely to escape when emitted at higher altitudes.

• spike55 says:

It doesn’t get a chance to re-emit in the lower atmosphere.

Re-emission time is several magnitude SLOWER than thermalisation.

Do at least TRY to keep up, little-ed.

• Ed Bo says:

When you present a graphic like that, it is usually considered good form to state what is being shown. Where were these measurements taken from? What exactly are they measuring?

I don’t think you even actually know. (Prove me wrong!)

• spike55 says:

YAWN

keep compounding your ignorance, little ed

dig deeper and deeper.

• Ed Bo says:

I see. You have absolutely no idea what information that graphic is displaying.

Typical!

• spike55 says:

Yes, we know you have absolutely no idea.

Basically all radiation below 11km comes from H2O

CO2 doesn’t re-radiate until above 11km

Seems you can’t even read a simple graph.

• Ed Bo says:

As I thought, you have no idea what that diagram is really saying. I will repeat what I said above: CO2 is emitting IR at all altitudes; it is just that it is much more likely to escape when emitted at higher altitudes.

How you can think that there is some magic switch that turns on CO2 emission at higher altitudes, but off at lower altitudes is beyond belief!

• spike55 says:

roflmao.

little ed doubles down on his ignorance

Cannot even read a simple diagram.

CO2 does not get a chance to re-emit in the lower atmosphere, the thermalisation time is several MAGNITUDES faster.

• rah says:

So Ed your saying that CO2 is a “blanket” that works only one way? IOW it lets LWR in but traps it when it’s reflected and tries to get out? Is THAT what your saying? The fact is that the blanket analogy for the atmosphere is now and has always been over simplified horse manure.

• Ed Bo says:

rah:

I was responding to squidly’s question: “Why can’t I just place a mirror in front of me to stay warm?”

I simply pointed out the empirical FACT that “mirrors” (highly reflective surfaces) are very commonly used to help people “stay warm”.

9. Rosco says:

If there is NO gravitationally induced temperature gradient why is it that every planet and moon we know in our solar system has a temperature lapse rate with altitude and the gas giants have “core” temperatures of thousands of degrees regardless of the fact that all of the outer solar system planets/moons receive almost no solar radiation and most contain no “greenhouse gases” ?

A lapse rate is a simple fact and no-one has proven it isn’t due to compression of a gas.

I’ll say again – what explains the lapse rate of Jupiter and the >25,000°C “core” temperature quoted by NASA if gravitational compression of the atmosphere is not the cause ?

• Ed Bo says:

All the planetary bodies in our solar system with atmospheres have atmospheres that are more transparent to incoming solar radiation than they are to outgoing longwave infrared. This means the atmospheres gain energy primarily from the bottom and lose it from the top.

This is the mechanism that creates the negative lapse rates we observe.

The gas giants still are losing thermal energy from their initial formation, as they emit more energy to space than they absorb from the sun (unlike the inner rocky planets like earth).

It is essential to distinguish the case of the initial dynamic compression, which does result in increased temperatures (Jupiter’s core got almost hot enough to initiate fusion), from the case of static pressure, which does not.

• spike55 says:

Not Venus. Its is warm at be base because of the gravity effect of its atmosphere.

And if the gravity based density-pressure-temperature gradient didn’t exist, warm air at the bottom would not rise.

That density-pressure-temperature gradient REGULATES how much energy is retained at any specific altitude.

• Ed Bo says:

spike:

Yes Venus! The negative lapse rate on Venus is caused by the FACT that its atmosphere is more transparent to solar radiation than it is to LWIR. A significant fraction of solar radiation makes it down to the surface, but virtually no surface IR makes it to space.

This effect is what CAUSES the negative lapse rate. Convection only LIMITS the lapse rate to adiabatic.

• rah says:

If that were true then Venus would continue to heat up and the surface temp would not remain relatively constant as it does. The mean surface temperature of Venus runs at 735 K (462 °C/863.6 °F) and is virtually constant, with little or no change between day and night, at the equator or the poles.

It’s the fact that the atmospheric pressure on Venus is 90x that of earth that is a primary factor that keeps Venus so consistently hot.

• spike55 says:

“A significant fraction of solar radiation makes it down to the surface”

RUBBISH. Not directly it doesn’t

The lapse rate is caused by gravitational auto-compression. And is calculated as such

• Ed Bo says:

spike, you say: “RUBBISH. Not directly it doesn’t”.

Ummm, the pictures sent back from the Venera spacecraft from the surface of Venus were taken in ambient sunlight. Emprical FACT. The Venusian atmosphere lets through a smaller fraction of sunlight than earth’s does, but it is still a “significant fraction” as I stated.

You say “not directly”. Are you seriously trying to claim that the Venusian atmosphere is so hot that it glows in the visible spectrum and provides visible light to the surface “indirectly”?

The negative lapse rate on Venus is caused by the same mechanism as on earth — the atmosphere gains energy mostly from the bottom and loses it mostly from the top. And the magnitude of the lapse rate is limited by the same mechanism as on the earth — if it is greater than adiabatic, it is “unstable” and convection brings it back towards adiabatic.

The fact that Venus has so much more atmosphere than the earth means that this adiabatic lapse rate from the level of emission to space down to the surface creates a much greater total temperature difference than is possible on the earth. (Which means that the alarmists claiming we could get a “runaway” warming on earth comparable to Venus are smoking crack.)

And to rah’s point, the fact that the thermal “resistance” to radiative loss from the surface to space is so high means that very little is lost during the night, and a lot of “mixing” between equatorial and polar regions has a chance to occur — much more than on the earth.

• spike55 says:

Oh dear, little ed is “so hot” because of the gravity based atmospheric compression

The surface does not receive any direct solar energy.

Do at least TRY to learn something. !

• Ed Bo says:

You won’t acknowledge your errors even when they are directly pointed out to you!

The pictures from the Soviet Venera probes are well known (and easily found). They were taken in sunlight.

Case closed.

• spike55 says:

What is the mean free path of CO2 emissions at surface pressures, little ed.?

Satellite at 400km or so distance?

Do some research, little-ed.

There can be no heat transfer without the heat differential already existing in the atmosphere

That energy gradient is caused by gravity causing a density-pressure gradient

ALL of which have been measured millions of times.

Your DENIAL of its existence and cause makes you look quite wacky !!

Now , do you have any empirical measurements for warming by atmospheric CO2?

• Ed Bo says:

spike, you ask: “What is the mean free path of CO2 emissions at surface pressures”?

Wait, above you have been arguing that CO2 doesn’t emit at all at surface pressures! I have been the one arguing that CO2 emits low in the atmosphere but it quickly gets re-absorbed. So I have been teaching you something!

Then you state: “There can be no heat transfer without the heat differential already existing in the atmosphere. That energy gradient is caused by gravity causing a density-pressure gradient.”

I take it you mean “temperature differential” where you say “heat differential”, as that is the only way that sentence makes any sense, but this is typical of your sloppy thinking.

But you are just plain wrong that this temperature differential is caused by gravity and its resulting density-pressure gradient.

We started this with a discussion of the persistent Antarctic temperature inversion, which is the opposite direction from what you assert gravity alone creates.

I pointed out that both Maxwell and Feynman trivially disprove your assertion, and they have gone unchallenged in the scientific community. You obviously think they are wrong. What is their error? How do you find an exception to the 2nd Law proof they give?

As to “empirical measurements for warming by atmospheric CO2”, I point you again to careful spectral measurements of downwelling LWIR at the surface under clear sky conditions. These show significant radiation in the 14-16 um band, which can only come from CO2. These spectral diagrams can be found in any atmospherci physics textbook. (You should read one sometime. You might actually learn something…)

And these measurements are often from thermal sensors, which hit a higher temperature when exposed to this radiation than when not.

• spike55 says:

“I have been the one arguing that CO2 emits low in the atmosphere”

And you are WRONG !!!

It doesn’t get a chance to.

Your DENIAL of the measured, observed, and calculated gravity based thermal gradient is quite hilarious.

Warming from increased atmospheric CO2 has NEVER been measured or observed ANYWHERE.

• spike55 says:

“These show significant radiation in the 14-16 um band, which can only come from CO2”

Another OOPS from little ed.

At earth temperatures (around 300 degrees Kelvin) the black body curve (or Planks curve) peaks at a wavelength of about 10um. The sides of the curve taper off at about 1um and 30um.

Carbon dioxide has fingerprint peaks at 2.7, 4.3
and 15um, which are all within the black body radiation curve.

The 15um is total absorbed and scattered.

Also overlaps part of the H2O spectrum of which there is FAR more in the atmosphere

• Ed Bo says:

spike:

I don’t know why I bother debating you when you argue so well with yourself.

The question you posed for me: “What is the mean free path of CO2 emissions at surface pressures” only makes sense if CO2 DOES emit at surface pressure.

Then when I point out that I have been stating that CO2 emits at surface pressure, you claim I am “WRONG!!! It doesn’t get a chance to!”

Make up your freaking mind!

You say: “Your DENIAL of the measured, observed, and calculated gravity based thermal gradient is quite hilarious.”

This comes after I have carefully and repeatedly explained why this thermal gradient is often observed, in a manner completely consistent with the laws of thermodynamics.

At times you actually agree with me, stating: “If … the surface is being warmed, then it keeps warming until that CONVECTIVE cooling starts.” Exactly what I have been arguing!

What about your DENIAL? Once again, make up your freaking mind!

I keep pointing out that the great physicists Maxwell and Feynman both explain trivially how the gravity-based explanation for the CAUSE (not the limiting) of the lapse rate leads to violations of the laws of thermodynamics. I keep inviting you to find fault with your arguments, and … CRICKETS!!!

I point out that that you can measure significant downwelling IR at the surface in clear sky conditions (and even in very low humidity) in the range of 15 um, and you counter with an argument that shows you have no clue what is going on.

First you (completely irrelevantly) bring up the 2.7 and 4.3 um-centered bands, without realizing that there is essentially no thermal IR from the earth in wavelengths that short. (Can’t you read a graph?) That is why nobody talks about these bands.

Then you argure that the 15um band is “total absorbed”, without understanding that emissivity equals absorptivity at any and all wavelengths.

The graph YOU display shows that water vapor over the entire height of the atmosphere does not absorb all of the 15um centered radiation band. But as you effectively argued elsewhere, the mean path of 15um radiation in typical CO2 concentrations is very, very short (< 1m at the exact center).

Once again, make up your freaking mind!!!

Look spike: you have a complete mishmash of (at best) half understood factoids without any underlying conceptual framework. That is why you continually and hilarious get things so wrong and often contradict your own arguments. Please, please, please, go off and spend a few years formally studying these topics. At the end of that time, you might have something constructive to contribute.

Until then, you are wasting everyone's time, including your own.

• spike55 says:

YAWN, still in DENIAL of a measured observed calculted (using just the gravity constant) thermal gradient.

If you haven’t got the brain-matter to comprehend, then maybe you should stop making a FOOL of yourself.

And STOP WATSING EVERYONE’S time with your anti-science DENIALISM

WOW.. just WOW. !!!

• spike55 says:

“thermal gradient is often observed, in a manner completely consistent with the laws of thermodynamics.”

WOW !!

, little ed FINALLY ADMITS that the gravity based pressure/thermal gradient exists !!!!!

Well done little ed. !!

• spike55 says:

“the mean path of 15um radiation in typical CO2 concentrations is very, very short (< 1m at the exact center)."

Yet satellite 400+km can pick It that radiation

roflmao !!

Talk about cognitive dissonance !!!

• Ed Bo says:

spike, you say: “little ed FINALLY ADMITS that the gravity based pressure/thermal gradient exists !!!!”

No, I have been arguing it all along, as you can clearly see if you re-read thread. See for example:

https://realclimatescience.com/2019/03/earths-energy-balance/#comment-200335

where I even show the magnitude of the adiabatic lapse rate (-g/cp).

I have finally figured out what your problem is. In my argument, this lapse rate is formed in Step 2, after differential lower heating. But you couldn’t make it to this step, as a two-step argument is beyond your comprehension.

You still haven’t explained your contradiction as to why you think the mean free path is relevant at STP when you also think there are no CO2 emissions at STP. Why not? It’s getting apparent that you can’t!

You still haven’t explained what you think is wrong in Maxwell’s and Feynman’s proofs that a lapse rate from gravity alone violated the laws of thermodynamics. Why not? It’s getting apparent that you can’t!

Seriously, I have worked with middle school science students who are more competent than you!

• spike55 says:

Middle school is about your standard little-ed

Gravity thermal effect EXISTS and controls the temperature gradient.

GET OVER IT !!

Your pathetic bravado and egotistical arrogance doesn’t alter this FACT.

• Ed Bo says:

I keep issuing this challenge to you, and for some reason you keep ignoring it! Surely it’s not a difficult task for someone as wise as you…

Copied from above:

“You still haven’t explained what you think is wrong in Maxwell’s and Feynman’s proofs that a lapse rate from gravity alone violated the laws of thermodynamics. Why not? It’s getting apparent that you can’t!”

One last chance to demonstrate you have the slightest clue…

• spike55 says:

Yawn, Poor little ed

DENIAL of what is measured, observed, and calculated using ONLY the gravity constant.

DENIES the density/pressure gradient that forms that temperature gradient

Poor CLUELESS little ed

• Ed Bo says:

Yep! As I thought, you don’t have a clue!

We’re talking about the temperature gradient, and you accuse me of “denying” the pressure gradient, when in fact I said early in this discussion: “Of course, there is a gravitationally induced pressure gradient — a very different issue.”

You don’t even understand the difference between pressure, density, and temperature!

And why don’t you answer my very simple question as to why you think those “deniers” James Clerk Maxwell and Richard Feynman were wrong???

10. dp says:

There is more up and side welling radiation from H2o and Co2 than down welling (molecules do not prefer any particular direction to radiate to) but nobody talks about it. This up welling radiation is how the Earth loses heat to space. Toss in some radiation extinction range numbers at all altitudes for the wavelengths being discussed plus some slant range of radiation in the presence of clouds and shadow lengths created and you quickly run out of math skills needed to discuss this.

• Squidly says:

I don’t need any math skills at all to invent a new swimming pool heater based on the so-called “greenhouse effect”. We know that standard glass is transparent to SWR (shortwave radiation) but opaque to LWR (longwave radiation).

Therefore, if I place a large sheet of glass say 8 feet above my pool, the SWR should heat my pool (as it normally does) but the LWR radiating away from my pool would hit the glass and “downwell” back to my pool, heating it even further. As a bonus, even when the sun goes down my pool is still radiating so that “downwelling” LWR should continue to heat my pool.

VIOLA !!! … free pool heating all year round !!! … by golly, I think I’m onto something here! … Oh wait, that’s right, an object (my pool) cannot heat itself !!! … I will leave it to the rest here to figure out why that is. The answer is so ridiculously stupid that I am astounded that this is topic is even of conversation anymore.

11. DH says:
12. angech says:

Interesting.
Lots of science but talking over each other.
There does exist a temperature /pressure/gravity relationship. And GHG
Fundamental physics.
They feed in both directions.
In other words if you want to consider gravity as a cause of temperature you can try it.
If you wish to consider GHG as a cause of temperature you can try it.
Both arguments have valid scientific pathways and both therefore are mutually dependent on the other being true.
Where we have a problem is when either side says only it’s viewpoint is valid and the other is wrong.
That leads to some imaginative twisting in the arguments here.
If you had an earth atmosphere with different levels of CO2 the temperatures would vary. The Temperature/Gravity [pressure] would also show the same variation, because with the addition of the CO2 and the rise in temperature the pressure changes that occur change the atmospheric mass the gravity is working on.

Ed Bo says:
“You still haven’t explained what you think is wrong in Maxwell’s and Feynman’s proofs that a lapse rate from gravity alone violated the laws of thermodynamics.”

Nothing wrong with Maxwell’s and Feynman’s proofs. Just a possible misunderstanding in application of their proofs which relate solely to the gravity discussed being held as a constant along with the atmospheric composition in isolation.
Gravity must vary as the atmospheric pressure [weight] varies due to the atmospheric composition so the lapse rate can be suitably affected.

• spike55 says:

“Gravity must vary as the atmospheric pressure [weight] varies due to the atmospheric composition so the lapse rate can be suitably affected.
–”

No, the lapse rate define PURELY in terms of the gravitational constant and the specific energy of the atmospheric composition.

In a dry adiabatic system it is pretty much a constant lapse rate.

In a wet system , ie H2O the lapse rate varies with the amount of water vapour, This proves that temperature different does NOT determine the lapse rate, and is actually a product of the gravity based thermal gradient.

Ed would be far better off if he tried to understand the actual physics instead of spending his time name-dropping.

End of conversation.

Its not worth my time trying to overcome such deep seated denialism.

Yap on, little ed.

• Ed Bo says:

angech:

Maxwell’s and Feynman’s proofs are very standard thermodynamic analysis, as anyone who has taken a serious thermo course would realize.

If, as spike asserts, gravity ALONE will create a lapse rate in an atmosphere, then it MUST be true that a thermodynamically isolated column of gas in a gravitational field would reach this lapse rate (-g/cp) in equilbrium, tending toward this lapse rate when not in equilibrium.

spike’s assertion thus leads to all sorts of violations of the 2nd Law of Thermodynamics. What Maxwell realized 150 years ago is that if you had two such isolated columns with gases of different cp value tightly thermally coupled at the bottom, they would have different temperatures at the top if the assertion were true.

So, if true, you could put a conductive wire between the tops of the two columns and it would conduct heat from the column with higher cp (and so higher temperature at the top) to the other column.

This transfer would put both columns out of equilibrium. spike thinks that both columns would automatically tend back to their (-g/cp) lapse rates, permitting the heat transfer in the wire to continue indefinitely. Which means he thinks there could be perpetual heat flow in an isolated system, which is a blatant 2nd Law violation.

I think it might be a little clearer if you put a thermoelectric generator in the middle of the wire. The spike’s analysis would have you believe that you could perpetually generate work from such a system, which is a ridiculous 2nd Law violation.

Feynman’s argument is even simpler, using a single isolate column with a conductive wire connecting top and bottom. spike’s analysis would lead to perpetually circulating current in that wire (that could drive a thermoelectric generator).

Note that neither of these analyses require the gravitational field to be constant, although there is only trivial variation of that field over the height of the atmosphere. Of course, there is a vertical pressure gradient in these systems, even with a constant gravitational field.

I find it very amusing that spike accuses me of denying basic physics when I am in agreement with two of the greatest physicists who ever lived. Feynman’s analysis is included in the best sellin physics text in history, studied by generations of students.

Now, I don’t believe in arguing from authority, so I have (repeatedly) asked spike to state what he thinks are the errors in Maxwell’s and Feynman’s analyses. He has completely refused to do so. Instead, he hilariously accuses me of “name dropping”.

This whole thread started when I pointed out that Antartica has a positive lapse rate (which is the opposite sign from adiabatic) for months every winter. spike and I agree that this is because the atmosphere is differentially cooled from the bottom in this case, due to the surface radiating away to space through a very transparent atmosphere.

Now, what would happen as you removed this differential cooling as spring approached? spike and I would agree, I think, that the atmosphere would first tend toward an isothermal (over height) condition, with the warmer upper atmosphere transferring energy to the colder lower atmosphere.

But spike believes that the atmosphere, without any additional inputs, would continue to transfer energy from the upper atmosphere to the lower atmosphere, EVEN THOUGH the upper atmosphere was cooler than the lower atmosphere. And that this would continue until the adiabatic lapse rate was achieved. (Note that the adiabatic rate is never exceeded here, so there is no convection.)

Anybody who understands the most basic concepts of physics would understand that this is in direct contradiction of the laws of thermodynamics. Talk about someone who needs “to understand the actual physics”!!!

(For the record, I will repeat my assertion that a negative lapse rate comes from the atmosphere being differentially heated from below and cooled from above, an effect that is dominant when the atmosphere has gases that are more transparent to shortware solar input to longwave surface output. You commonly see the – g/cp adiabatic lapse rate in such a system because any gradient greater than adiabatic causes convection, which REDUCES the magnitude of the lapse rate back toward adiabatic.)

• spike55 says:

“But spike believes that the atmosphere, without any additional inputs, would continue to transfer energy from the upper atmosphere to the lower atmosphere,”

Now you are just making CRAP up.

Oh wait, you have been doing that all along !!!

“You commonly see the – g/cp adiabatic lapse rate in such a system because any gradient greater than adiabatic causes convection,”

WOW, FINALLY.

Yes , gravity controls the energy transfer, hence sets the lapse rate and therefore the temperature gradient.

You ALWAYS see the -g/cp lapse rate in every sufficient atmosphere, because gravity is the control of the thermal gradient

The temperature gradient can be calculated DIRECTLY from gravity in a dry atmosphere

I knew you would figure it out eventually, little-ed, even if by accident.

Well Done :-)

• Ed Bo says:

spike, you say “Now you are just making CRAP up.

So let’s break it down into baby steps that you can understand.

You believe that gravity ALONE will create the adiabatic lapse rate in the atmosphere.

This means you MUST believe that a thermodynamically isolated column of gas in a gravitational field will be driven toward the adiabatic lapse rate from a different lapse rate.

This means you MUST believe that if you have a thermodynamically isolated column of gas that starts out in isothermal conditions in this gravitational field, it will be driven toward the negative adiabatic lapse rate.

This means that you MUST believe that in this thermodynamically isolated column (no energy or mass exchange with the rest of the universe) that is tending toward adiabatic, that energy is being transferred from the colder upper regions to the hotter lower regions.

This is a DIRECT implication of your beliefs. No way around it! Such a result should make you re-examine your beliefs, but noooo…..

And you continue to completely misrepresent what I say, in such a blatant way that it must be intentional. You quoted the middle of my final paragraph, cutting out the beginning and end, to deliberately distort my argument. So once again:

For the record, I will repeat my assertion that a negative lapse rate comes from the atmosphere being differentially heated from below and cooled from above, an effect that is dominant when the atmosphere has gases that are more transparent to shortware solar input to longwave surface output. You commonly see the – g/cp adiabatic lapse rate in such a system because any gradient greater than adiabatic causes convection, which REDUCES the magnitude of the lapse rate back toward adiabatic.

Someone with real arguments does not need to stoop to such tactics.

• Ed Bo says:

Don’t know how that picture got attached. It is funny though, especially with noted alarmist Seth Borenstein in the byline.

• spike55 says:

Yep, stick to your baby steps.

All you have.

Measured, observed, calculated using ONLY gravity, on every planet in the solar system with a viable atmosphere.

NOT calculated by temperature differentials.

Why do you continue to swim in DENIAL.

• Ed Bo says:

spike:

Upthread, you agreed that if surface heating started to create a negative lapse rate larger than adiabatic, convection would kick in to drive the lapse rate back to adiabatic.

You have presented NO argument that says that this differential heating inducing convection is not the reason we commonly (but not universally) see the adiabatic lapse rate in atmospheres.

And I’m still waiting with bated breath for your explanation of how an atmosphere with a small negative lapse rate automatically evolves to one with the larger negative lapse rate through gravity alone, requiring net transfer of energy from the cooler upper atmosphere to the warmer lower atmosphere.

What equations do I use to calculate the rate of this transfer? I can’t find it in any of my physics, thermodynamics, or heat transfer textbooks. They only have equations that calculate the rate of transfer from warmer to cooler!

Waiting…

• Douglas Hoyt says:

In Maxwell’s two column experiment, the pressure at the base of the two columns would be different, so there would be a flow from the higher pressure column to the lower pressure column, or else someone is doing work to keep the base of the two columns at equal pressure.

• Douglas Hoyt says:

Just to clarify, the two columns are of the same height and have the same number of molecules. Thus one column will weigh more than the other, since molecules with different values of Cp have different molecular weights. Different column weights, hence different pressures at the base of the columns.

The experiment seems be poorly described.

• Ed Bo says:

Douglas:

In Maxwell’s thought experiment, the two columns of gas are mechanically separated, but thermally connected (by a highly conductive member at the bottom to ensure the two columns have the same temperature at the bottom, and a thin wire at the top).

So there is no pressure-induced flow at the bottom.

• Douglas Hoyt says:

Highly conductive? It would have to be a superconductor. That requires external energy to maintain, so no perpetual motion machine.

These one dimensional models are irrelevant to a three dimensional planet with time varying inputs of heat.

• Ed Bo says:

Douglas:

Metals are highly conductive without being superconductors requiring external energy.

The thermal conductivity of copper is 385 W/m/K. The thermal conductivity of air at STP is about 0.024 W/m/K. So standard copper is 15,000 times more conductive than air.

So a copper bar connecting the bottoms of the two columns could easily keep the gas at the bottom of the columns at essentially the same temperature, conducting away any difference thousands of times faster than the higher air could possibly re-create a difference.

This brings up an interesting question. For those who believe the natural equilbrium of a column of gas in a gravitational field, even in isolation, is the adiabatic lapse rate, what is the rate of conductive heat transfer from the colder top to the higher bottom? You can’t use Fourier’s Law of thermal conduction employing the 0.024 W/m/K air conductivity. That doesn’t even work in the needed direction.

But I’m sure spike will have an answer for us. He’s always very fast to supply a real answer when challenged…

• Douglas Hoyt says:

The copper bar will dissipate heat. Your perpetual motion machine will grind to a halt.

Also the vertical columns will need to be perfect insulators, or else heat will escape causing your perpetual motion machine to grind to a halt, or else heat will enter, destroying it, all depending upon outside conditions. The Maxwell thought experiment can never be built in reality. It is poorly conceived.

Again, one dimensional thought experiments are irrelevant.

• Ed Bo says:

Douglas:

I’m afraid you don’t even understand the concept of dissipation. In thermodynamics, dissipation is the conversion of “organized” energy (“work”) to “disorganized” energy (“heat”). So if you had electrical current (organized energy) in the copper bar, its electrical resistance would convert some of that organized energy to disorganized thermal energy.

But we’re talking here about the transmission of already disorganized thermal energy through the copper bar. There is nothing to dissipate here. And it’s very easy to insulate to keep this energy transfer essentially all inside the bar, given the very high thermal conductivity of copper relative to air.

By the way, your mentioning of superconductors in a previous comment underscores your level of confusion. “Superconductors” are super-electrical-conductors, not super-thermal-conductors.

And you completely miss the point about thought experiments. They, like many idealized laboratory experiments, serve to isolate a particular effect from the messiness of the real world for detailed analysis.

And this thought experiment of Maxwell’s was key in his development of the kinetic theory of gases, and of the Maxwell-Boltzmann distribution of gas-molecule velocities required for it. Both of these are completely unchallenged in the scientific world for over a century.

• Douglas Hoyt says:

Your thought experiment is missing so many aspects of physics that it is worthless.

There no need for any further discussion with such an ignoramus.

• Douglas Hoyt says:

Also if you put insulation around your copper wire, it will not be perfect, but will lose heat to its surroundings. That is dissipation which you have no idea what it is.

In a thought experiment you can’t just pick and chose some aspects of physics and neglect other aspects of physics. If you do, your thought experiment becomes worthless – just a fairy tale.

Again, your worthless one dimensional thought experiment has nothing to do with a three dimensional system.

• Ed Bo says:

Douglas:

You say: “Your thought experiment is missing so many aspects of physics that it is worthless.”

It’s not my thought experiment, it’s James Clerk Maxwell’s. And as I said before, it led to several key scientific advances.

Then you say: There no need for any further discussion with such an ignoramus.

A guy who doesn’t understand the difference between thermal conduction and electrical conduction calling one of the greatest scientists of all time an “ignoramus”? That takes real gall!

Here’s the reason this thought experiment is useful and valid in this context. We are discussing why the adiabatic lapse rate is commonly seen in atmospheres. People like spike believe that gravity alone can create a negative lapse rate. I believe that you must have differential warming of the atmosphere from the bottom and differential cooling from the top to create a negative lapse rate.

To choose between the two theories, we can imagine a scenario where there are no heat transfers into or out of the atmosphere. I believe that such an atmosphere would be isothermal in equilibrium. spike believes this atmosphere would have the adiabatic lapse rate in equilibrium.

So how do we think about this idealized case? Well, it turns out Maxwell did so in the 19th century. He started by assuming spike’s theory was correct, and followed the implications of it. He found it led to a direct violation of the 2nd Law of Thermodynamics. (This led him to re-examine, and eventually discard, his first equations for the kinetic theory of gases, as they predicted a negative lapse rate in equilibrium.)

Since spike believes that no heat transfer is necessary for the adiabatic lapse rate to form (that is, it would form in this idealized isolated column), I have challenged him to identify the physical mechanism by which this could happen, starting from a static isothermal column. He has not provided any suggestions for such a mechanism.

I repeat that the use of these idealized cases is very valuable (not worthless, as you say) in many fields of science to isolate particular effects. It was used over and over in my thermodynamics and heat transfer courses. If you had ever studied these topics formally, you would be well aware of that.

• Douglas Hoyt says:

I never said electrical conduction and thermal conduction were the same, so stop putting words in my mouth.

You’re the one defending a thought experiment that has numerous violations of the laws of physics. A thought experiment like that can not tell us anything worthwhile. Hence, it is worthless.

• Ed Bo says:

Douglas:

In a discussion about thermal systems, YOU introduced the idea of superconductivity, which is an electrical property, not a thermal property. YOU argued about energy dissipation as a function of conductivity, which is a phenomenon of electrical systems, not thermal systems.

You were, AND STILL ARE, completely confused. And yet you presume to call Maxwell’s important analysis “worthless”.

Do you seriously consider the derivation of the kinetic theory of gases, including the Maxwell-Boltzmann distribution, “worthless”???

• spike55 says:

“starting from a static isothermal column.”

starting from something that doesn’t exist ??

wow, bizarre land in ed’s head. !!

show us Maxwell’s thought bubble as an actual real experiment, little-ed.

show me where this exists in the atmosphere, little-ed.

oh and… Do you still think that holding up a 100kg weight doesn’t take any energy, so long as the weight is stationary ?

You have a BIZARRE concept of reality. !!

• Ed Bo says:

spike:

You agree that positive lapse rates (temperature inversions) sometimes exist. For this condition to change to a negative lapse rate, it must pass through the condition of zero lapse rate (isothermal). I know this is a difficult concept for you, but please try to wrap your head around it!

Elsewhere we have dealt with your fundamental confusions between force, energy, and power. You get them wrong at the most basic level, no matter how many times the difference is explained to you.

I have pointed out that my desk requires no power source to hold up a 100kg weight. There is a steady FORCE of 980 Newtons required, but there is no energy transfer or energy expenditure required to hold the weight static.

I have pointed out the most basic physics equation for the energy transfer in this situation is:

Work (energy) = Force * Distance

Since this is a static situation, the distance is zero, so the work is zero.

I have many times asked you for an actual analysis of your alternative ideas, and you have never provided any. Your silence speaks volumes!

• spike55 says:

but there is no energy transfer or energy expenditure required to hold the weight static.

ROFLMAO. !!

Really?,,,, little-super-Ed.

Holding a 100kg barbell over your head takes no energy at all , so long as its stationary !

Please send pictures of you doing this. (lol)

100kg, held above your head for 10 minutes.

I mean, a 5 year old could do it, right little-super-ed ;-)

Takes no energy, afterall , right little-super-ed. ;-)

So funny, so ANTI-reality.

Just like holding a 10km+ column of air up, takes no energy at all, so long as its stationary.

You poor silly reality-challenged nil-educated little twerp.

• spike55 says:

super-ed thinks he can hold a 100kg weight above his head without expending any energy

HOW DUMB IS THAT !!

super-ed. the weight has a CONSTANT downwards force of 980N

To hold it steady, you have to provide a CONSTANT 980N upward force.

Where does that force come from?

Forces don’t come from “nowhere” you know !

Do you ROOOLY , TROOLY believe it doesn’t take any energy to hold a 100kg weight stationary above your head.

Have you ever tried it?

Truly BIZARRE !!!

• Ed Bo says:

spike:

Why do you keep ignoring my counterexample of my desk supporting 100kg without any ongoing power transfer?? Is it because it completely demolishes your analysis?

If something (anything!) can support this 100kg without ongoing power expenditure, then obviously this ongoing power expenditure cannot be a REQUIREMENT of the task as you assert. This is not a difficult concept!

Consider a motorized winch holding up a 100kg weight by a cable. You attach a power meter to the electrical cord supply the motor. With the motor active, you measure current and power into the motor. Let’s say its 120 volts and 1 amp, so 120 watts expended holding up the weight. You claim vindication!

But next we engage the brake on the winch, and remove the power from the motor. Now we have 0 amps and 0 watts into the motor. But it is still holding up the weight! So it CANNOT be a fundamental requirement that ongoing power is required to hold up the weight.

The winch with the active motor holding up the weight is like the person holding up the weight. It has LOSSES in generating the force.

But the winch with the brake engaged holding up the weight is like the desk holding up the weight. It has no losses in generating the support force.

In both cases, it is clear that there is no ongoing power transfer REQUIRED to support the weight.

Whenever I ask you for particulars, you always evade the question. But I will try one more time. How much power (in watts) do you think is required by the desk to statically support the 100kg weight on top of it? Please show your work.

Here is my analysis and answer:

Power (W) = Force (N) * Velocity (m/sec)

Power (W) = 980 N * 0 m/sec = 0 W

And if your answer yields a non-zero power value, please indicate the power source for the desk.

Should be simple for a genius like you.

• spike55 says:

“Why do you keep ignoring my counterexample of my desk supporting 100kg without any ongoing power transfer??”

roflmao.

Because it shows you know NOTHING about structural mechanics. Your ignorance is really starting to show, for everyone to see. :-)

When you hold the 100kg weight above your head, you have to produce and equal and opposite force to hold it in place.

Where does that force come from? super-ed ?

When the 100kg weight is sitting on a table, the table MUST be exerting an equal and opposite force (980N) on the weight. Right little-ed?

Where does the table get that force from ?

What if the table is made of thin balsa wood ?

YOU HAVE A LOT TO LEARN, little-ed.

… and until you do, you really ought to just stop digging yourself deeper and deeper into your pit of ARROGANT IGNORANCE

• spike55 says:

SO HILARIOUS that you think the physics is any different for a person holding a 100kg weight stationary , vs, a table holding a 100kg weight stationary.

JUST DUMB, actually !!!!!

• spike55 says:

please indicate the power source for the desk.

And therein lies your ABJECT IGNORANCE of materials and structures, and why you are INCAPABLE of understanding how the gravity thermal gradient is formed.

I know where the energy comes from for the desk to apply an upward force equal to the downward force of the 100kg mass, WHICH IT MUST DO.

Or do you actually DENY that the desk is exerting an upward force ???????

Its up to YOU to further YOUR education and find out for yourself.

hint: It comes from the same place as the energy you MUST use to counter the downward force of that same 100kg held stationary above your head.

• spike55 says:

Poor little super-ed probably thinks he could hold a 50lb longbow fully drawn without using any energy.

I mean, its stationary isn’t it, super-ed. ;-)

• Ed Bo says:

spike:

As soon as I ask for a definite answer from you, you furiously evade. The typical trick of someone who has no actual argument.

Also, you repeatedly misstate my arguments. Another typical trick of someone who has no actual argument.

I have carefully distinguished the cases where producing the force creates power losses (active winch, person) and those in which it doesn’t (braked winch, desk). The mere EXISTENCE of case in which it doesn’t completely disproves your arguments.

I reviewed one of my old structural mechanics texts (Timoshenko and Gere). There is NOTHING in it that confirms your arguments.

Tensile strength is NOT power transfer. Compressive strength is NOT power transfer. Elastic strain energy REQUIRES motion to change.

You claim that I am wrong that without motion, force does produce any power transfer. If my error is so fundamental, it should be trivial for you to provide your own answer from out of technical textbooks. But every time I ask you…crickets!

I wonder why?

13. angech says:

“Anybody who understands the most basic concepts of physics “.
Includes most everybody.
and Maxwell.
“Maxwell’s demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated”
Gravity has effects which can induce tides and friction and hence give heat. Most places with the maximum of gravity in normal space, cue suns, are hottest centrally.
There is a relationship of gravity, pressure and temperature.
Causality is much harder to define.
Not sure which of the 5 you are.

• Ed Bo says:

angech, you say: “Gravity has effects which can induce tides and friction and hence give heat.”

Gravity must create motion to do this — it must cause things to fall. We’re talking here about a static column of gas. No motion created by the gravitational force, no energy transfer.

• spike55 says:

Oh look, little-ed is one of these funny little people who thinks he can hold up a 100kg weight, and so long as he holds it stationary, it doesn’t require any energy.

How does little-ed go through life with so little understanding of reality. ??

Quite BIZARRE !!!

• Ed Bo says:

Oh no, not that ridiculous canard again!

spike: “I require continuous power output to hold up a 100kg weight static against gravity. Therefore it is an absolute requirement that everything requires continuous power output to hold up a weight against gravity.”

Ed: “My desk is doing a fine job holding up a 100kg weight static against gravity. And it requires no continuous power output to do so. In fact it has no power source that could let it do so.”

The trivial and totally obvious example of my desk completely disproves your analysis. (And no, the one-time increase in elastic strain energy from the weight non-statically compressing the desk when laid upon it, does not provide any basis for ongoing power output.

As I have pointed out numerous times before, you are completely confused about the difference between force, power, and energy. And these are concepts that mediocre high school students grasp easily!