How is it possible that Thermosphere can maintain so much heat?

Question

Thermosphere is the Layer of Atmosphere in approx 100-1000 km altitude. Particles in thermosphere are typically at 1400 K temperature. But the sun activity can raise the temperature up to 2300 K.

It's already answered here, that the heating would be caused by a Solar XUV radiation; Temperature rise in Thermosphere

Without making any statement about the cause of this heating, I decided to calculate the cooling by (black body) radiation, and that way define the energy amount needed to maintain this temperature.

First I needed to estimate amount of particles in Thermosphere. I decided to calculate it my self too, and found a range of $7x10^8 kg$ to $3x10^{13}kg$ when I used ie. this source. If we use plain wiki for atmosphere, we found that it would be 0.00003% of $5.1480×10^{18} kg$ also $1.54x10^{14} kg$

Second I needed to estimate how much radiating surface this mass have.
I Chose "N", nitrogen. Molar mass $14g/mol$ so we are in a range of $5x10^{10} mol$ to $2x10^{15}mol$
If we calculate the sphere with the Van der Waals radius of Nitrogen, we have $3x10^{-19}m^2$ pro particle.
Which multiplied with the mol amount and particle amount/mol $6x10^{23}$ provides a range for radiating area; from $9x10^{15}m^2$ to $9x10^{21}m^2$

Third We need to calculate the Radiating power $W/m^2$, this is based on the black body radiation by Stefan-Boltzmann law. The equation is really simple, we basically need only temperature; The Average is $1400 K$, which means $220 kW/m^2$ and the peak $2300 K$ makes it up to $1600 kW/m^2$

Fourth We just wonder what is the power, the range is from $2x10^{21}W$ to $2x10^{27}W$

WHAT? It's more than Sun, which has a Power of $3.846×10^{26} W$ Sounds impossible at first sight, I try to avoid mentioning the https://physics.stackexchange.com/questions/220050/le-sages-theory-of-gravitation-is-drag-the-only-reason-why-this-theory-fails as it said it fails because of the Energy problem....

...as the Gravitational Binding energy of Earth is in an order of $2.487 x 10^{32} J$; Million time more than the Sun's radiating power!

My Question;
How it is possible that Thermosphere can maintain so much heat? (Heat = The amount of energy in a system)

As some might think how it's even possible that Space is radiating with a higher power than Sun. Thus it might be helpful to mention that fusion is based on mass is based on Volume, but the radiation is based on the surface amount. And as for a Sphere $A=4\pi r^2$ and $V=4/3\pi r^3$, thus you can increase the surface amount enormously be reducing the particle size.

Explaining picture;

At the picture the Thermosphere is the Red ring around the blue Earth. As below and above it, the Atmosphere/space is colder, it can be asked that Why is the Sun heating only this part of Space molecules, and not also the part shown with red arc and question mark?
And not to be forgotten, that Earth is moving with an average orbital Speed of approx 30 000 m/s, which practically means that in only 30 seconds the whole Thermosphere could have new, cold particles from the space. This statement is provocative, as the gravity is ofcourse "holding the atmosphere". But please think a while; as Gravity doesn't push the particle up on the direction of the orbital velocity vector, it might rather be expected that these Particles flows around Earth laminar-alike. If the Gravity would be working according to Le Sage's, then there would more particles coming to the sun side. (red arrow) This would rather explain the Heat difference between day and night, as the required heating power is in order of $TW/m^2$ compared to the order of $kW/m^2$ provided by the sun.

Answer 1

The thermosphere has a high temperature because each particle in the thermosphere has high kinetic energy. But this does not mean the thermosphere is hot. Heat is a measure of the total energy per unit volume, while temperature is a measure of the average kinetic energy of each particle in a system. Here is a link that explains the difference: http://www.theweatherprediction.com/habyhints/39/.

There is a fundamental difference between temperature and heat. Heat is the amount of energy in a system. The SI units for heat are Joules. A Joule is a Newton times a meter. A Newton is a kilogram-meter per second squared. Heat is transferred through radiation, conduction and convection. The amount that molecules are vibrating, rotating or moving is a direct function of the heat content. Energy is transported by conduction as molecules vibrate, rotate and/or collide into each other. Heat is moved along similar to dominos knocking down their neighbors in a chain reaction. An increase of electromagnetic radiation into a system causes the molecules to vibrate, rotate and/or move faster. With convection, higher energy molecules are mixed with lower energy molecules. When higher energy molecules are mixed with lower energy molecules the molecular motion will come into equilibrium over time. The faster moving molecules will slow down and the slow moving molecules will speed up.

Temperature is the MEASURE of the AVERAGE molecular motions in a system and simply has units of (degrees F, degrees C, or K). Notice that one primary difference between heat and temperature is that heat has units of Joules and temperature has units of (degrees F, degrees C, or K).

When you say the thermosphere is "so hot", I think you are confusing temperature with heat. The high average temperature of its diffuse particles is strongly influenced by whether the Sun is shining on it, and by how active the Sun is at any given time. For example, the temperature of the thermosphere is about 200 degrees C greater during the day than it is at night, and its temperature also can be as much as 500 degrees C greater when the Sun is very active. Because the density of particles in the thermosphere is low, it doesn't hold much heat. As CuriousOne says in his comment, the thermosphere is not in thermal equilibrium.