Density of an ionised gas

In summary, the conversation discusses the problem of finding the resulting density of a gas consisting of n atoms with individual mass m and charge q under external pressure, assuming spherical symmetry. It is determined that the density can be calculated using the equation \rho = \frac{mn}{V_{gas}}, where V_{gas} = n \cdot 4/3 \pi a^3 and the internal pressure of the gas is equal to the external pressure. The application of Coulomb's law is verified and used to calculate the internal pressure.
  • #1
MikkelR60
1
0
I have been wondering about this problem for quite some time now and any input is much appreciated. If a gas consisting of n atoms with individual mass m and charge q is put under an external pressure P what will the resulting density be? Assume spherical symmetry.

An illustration of the problem (The external pressure is supplied by an electrically charged sphere)
es_sphere.JPG


The density of the gas must be
[tex]\rho = \frac{mn}{V_{gas}}[/tex]

If there is an average space of a between the atoms (and let's assume that the atoms does not occupy any space) then the total space occupied by the gas is Vgas = [tex]n \cdot 4/3 \pi a^3[/tex].

The internal pressure of the gas must be equal to the external pressure.
Fext = Fint
PA = [tex]n \cdot \frac{1}{4 \pi \epsilon_0} \frac{q^2}{a^2} [/tex]
From here its just substituting and expressing rho in terms of the stated variables.

Can someone please comment on my derivation, does it seem sound? I am most concerned with the application of Columbs law.

All the best
Mikkel
 
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  • #2
Your derivation seems sound. The application of Coulomb's law is correct and it allows you to calculate the internal pressure of the gas given the external pressure. To get the density, then use the equation \rho = \frac{mn}{V_{gas}} and substitute in for V_{gas}.
 
  • #3


Your derivation seems sound and correctly applies Coulomb's law. However, it is important to note that the resulting density will also depend on the temperature and the type of gas being considered. For an ionized gas, the density will also be influenced by the degree of ionization and the presence of any external electric or magnetic fields. Additionally, the assumption of spherical symmetry may not always hold true in practical situations, so the resulting density may vary depending on the actual shape and arrangement of the gas molecules. It would be beneficial to consider these factors in your analysis as well. Overall, your approach is a good starting point for understanding the density of an ionized gas, but further considerations and calculations may be necessary for a more accurate and comprehensive understanding.
 

1. What is the definition of density of an ionised gas?

The density of an ionised gas refers to the amount of mass per unit volume of a gas that has been ionised, meaning it has lost or gained electrons and become charged particles.

2. How is the density of an ionised gas measured?

The density of an ionised gas is typically measured using a specialized instrument called a mass spectrometer, which can determine the mass and charge of individual particles in a gas sample. The density can then be calculated by dividing the mass by the volume of the gas.

3. What factors affect the density of an ionised gas?

The density of an ionised gas can be affected by a variety of factors, such as temperature, pressure, and the types and number of particles present in the gas. Additionally, external factors like electric and magnetic fields can also impact the density of an ionised gas.

4. How does the density of an ionised gas differ from that of a neutral gas?

The density of an ionised gas is typically lower than that of a neutral gas, as the ionisation process removes some of the mass and decreases the number of particles in the gas. However, the density of an ionised gas can increase in the presence of strong electric or magnetic fields.

5. What are some real-world applications of studying the density of ionised gases?

The study of the density of ionised gases has many practical applications, such as in plasma physics, astrophysics, and the development of fusion reactors. It is also important in atmospheric science, as ionised gases in the upper atmosphere can affect satellite communication and other technologies. Additionally, understanding the density of ionised gases is crucial in fields like semiconductor manufacturing and laser technology.

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