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Plasma is the fourth state of matter. Wikipedia says, that all the gaseous atoms will be ionized into positive ions and free electrons at extremely high temperatures. But, what does this explain in a plasma-globe and other applications. Do all these artificial apps have a relation with the plasma in stars...? If so, how is this high temperature maintained in such a small area?

If this relation is perfect, then plasma could be used for conduction of electricity, as it has extra-ordinary number of free electrons. Am I correct in stating that plasma conducts electricity very well?

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The ions and the electrons don't necessarily have the same temperature (non-thermal plasma), but if you leave them for a while, they will undergo equilibration. I would not overestimate the value in Kelvins of different degrees of freedom of subsystems. The temperature is associated with a mean kinetic energy. If you tackle an electron, you can accelerate it easily because of its low mass. Conversely, even a fast electron will not give raise to the same momentum transfer as a heavy particle. So a fast electron is "not as powerful" as an equally fast ion.

If you have an application like the ball, there the effect is mainly generated by accelerating of electrons in the electric field. If you go away from the electrodes, the field gets weaker and there the electrons lose their kinetic energy due to collisions with heavier particles. This is why a too high particle density (or pressure) is not the friend of open corona discharges - the glow effect can't extend too far away without an opposing charge somewhere else, such that there is a relevant electric field in between. Of course, if the temperature is generally high (thermal plasma) as in the sun, then you will have charges flying around in any case. But for the earthly applications you have in mind, the area containing free electrons/ions doesn't extend forever and the temperature will not kill you unless the electric field that produced it is super strong.

Then as Shaktyai pointed out, plasmas are not always totally ionized, usually the opposite is the case. For some cases the Saha equation holds and there you get an idea about the functional dependence of the ionization degree with temperature. For high $T$, the factor goes against 1 (graph exp(-1/x) in wolfram alpha or so).

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Plasmas are not necessarily a mixture of totally ionized gas. Plasmas are gas sufficiently enough ionized to exhibit characteristic waves and other collective behaviors. A simple flame is a plasma though the temperature is far below the ionization temperature (around 10000 K). Such plasmas are called cold plasmas. To produce it, one can use a strong electric field. Glowing electric bulb tub, globe ball, or plasma torch are typical examples. In stars (more generally in fusion plasmas),the temperature is very high, far above the complete ionization threshold. The heat is released by the nuclear fusion reaction. Such plasmas are called hot plasmas. Plasmas are indeed good conductors but they are not great conductors. They have about the same resistivity as copper. In Tokamak fusion reactors, the heat released by joule-heating effect is used to heat the plasma.

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@ Crazy Buddy: Thank's for your edits. English is not my native language. –  Shaktyai Aug 20 '12 at 6:56
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Highest of high temperature can exist in smallest volume. Besides there are ways to produce plasma, one is to keep on heating it (Stars do this), this is inefficient. Other is feeding electric energy to electrons to hit neutrals and ionize it. Now all this plasma globe and etc the temperature is room temp only. The electron gets high temperature up to 20000 degree K, but there only 1 or 2% of total gas is ionized. so it doesn't matter high temperature but total heat is small. Also those 1 or 2 % ions are at room temperature unlike hot electron.

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