# Will ideal gas law apply to plasma?

I have read that plasma is a state of matter that resembles gas but it consists of ions and electrons coexisting. So my question is : If plasma is just ionized gas, will ideal gas law apply for it ?

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Electrically charged particles interact via their fields and so there is, in general, wide range interaction throughout the gas. The electromagnetic interactions between particles of the gas/plasma can give raise to effects which are significantly different from neutral gas, such as e.g waves. So to what extend the ideas gas law can be considered to "hold" for a plasma will depend on the parameters of the system, temperature, pressure, etc., but foremostly of the ionization degree of the gas/plasma.

It's an involved issue, as this quantity will depend on all the other parameters. One commonly cited relation for certain parameter ranges is the Saha equation, which relates temperature and particle density - which are both part of $PV=k_B T\cdot N$ too. Microscopic considerations in such a "chemical system", where the constituents can be ionized and thereby change their properties, lead you to the observation that the value charge density depends on the surroundings. So e.g. the Poission equation takes a nonlinear form $\Delta\Phi=\rho(\Phi)$.

It's then also related to new'ish system parameters like the Debye length, which caracterize the overall bahaviour you ask for. I'm sure there are Debye length-temperature ranges where it's perfectly reasonable to apply a gas law, just watch out which part of the system makes up charged particles or neutral ones. E.g. I think in space, there are a whole lot of charged particles, but people work with ideal gas laws.

A general rigourous classical look at it will lead you to $PV=k_B T\cdot \text{ln}(\mathcal Z)$, where the partition function contains the Hamiltonian of the system, which include the potentials $\Phi$ = energy expressions involving multiple variable-integrals over statistically weighted interaction potentials, see this link.

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I just need to know if the generals rules apply, e.g If pressure and volume are inversely proportion, pressure and temperature are directly proportion? –  Abdelrahman Esmat Nov 9 '12 at 21:11
@AbdelrahmanEsmat: In general no. This relates to the virial expansion mentioned at the end of the last link. –  NikolajK Nov 9 '12 at 22:13

No. An ideal gas means that interaction is negligible. This is not the case for the electromagnetic interaction of charged particles, hence not in a plasma.

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