What equivalence of vacuum in pressured system is possible?

[BernieM]

If I have a volume of gas in a sealed container with a special one way valve in it, and I heat the gas inside the container, the pressure increases and some gas escapes through the valve to the outside. I now have less atoms of gas inside the container, which, when cooled back to the starting temperature will be a partial vacuum. If I continue to heat the gas in the container higher and higher, what is the maximum equivalent vacuum that I could obtain?

Is the limit going to be the maximum temperature I can obtain in the gas? Or some other physical limit? With enough power to create sufficient heat, could I in effect reach a state, for example, of 10 -6 torr, as far as the number of atoms in the volume and at the same time be maintaining an internal pressure equivalent to the pressure outside the container?

So to avoid 'practicalities' of the valve, let's say it works on effusion or in some ideal way that would not let any molecules back into the chamber and that the chamber material and construction is some ideal container that can withstand any temperature and doesn't pass any heat through it's walls to the outside so there is no loss of heat there.

 

[Chestermiller]

Why don't you just run some calculations on your own using the ideal gas law and see what you come up with?

 

[BernieM]

I wasn't sure it was valid at all temperatures where the atoms become a plasma.

From Wikipedia:
Deviations from ideal behavior of real gases
The equation of state given here applies only to an ideal gas, or as an approximation to a real gas that behaves sufficiently like an ideal gas. There are in fact many different forms of the equation of state. Since the ideal gas law neglects both molecular size and intermolecular attractions, it is most accurate for monatomic gases at high temperatures and low pressures. The neglect of molecular size becomes less important for lower densities, i.e. for larger volumes at lower pressures, because the average distance between adjacent molecules becomes much larger than the molecular size. The relative importance of intermolecular attractions diminishes with increasing thermal kinetic energy, i.e., with increasing temperatures. More detailed equations of state, such as the van der Waals equation, account for deviations from ideality caused by molecular size and intermolecular forces.

So since I was wondering for example how hot I would have to heat the gas to get it to the equivalence of atoms / cubic centimeter to a vacuum of 1e10-6 torr or better, I figured it was going to have to be very very hot (millions of kelvins) and hence my question of what may be the barrier to that that I was not aware of.

 

[Chestermiller]

I wasn't sure it was valid at all temperatures where the atoms become a plasma.

From Wikipedia:
Deviations from ideal behavior of real gases
The equation of state given here applies only to an ideal gas, or as an approximation to a real gas that behaves sufficiently like an ideal gas. There are in fact many different forms of the equation of state. Since the ideal gas law neglects both molecular size and intermolecular attractions, it is most accurate for monatomic gases at high temperatures and low pressures. The neglect of molecular size becomes less important for lower densities, i.e. for larger volumes at lower pressures, because the average distance between adjacent molecules becomes much larger than the molecular size. The relative importance of intermolecular attractions diminishes with increasing thermal kinetic energy, i.e., with increasing temperatures. More detailed equations of state, such as the van der Waals equation, account for deviations from ideality caused by molecular size and intermolecular forces.

So since I was wondering for example how hot I would have to heat the gas to get it to the equivalence of atoms / cubic centimeter to a vacuum of 1e10-6 torr or better, I figured it was going to have to be very very hot (millions of kelvins) and hence my question of what may be the barrier to that that I was not aware of.

Your assessment seems correct. For the pressures you are interested in, the ideal gas law would be adequate. Of course, integrity of the container would be an issue at those kinds of temperatures.

 

[CWatters]

If I continue to heat the gas in the container higher and higher, what is the maximum equivalent vacuum that I could obtain?

In order for gas to escape, the pressure inside when hot must be greater than the pressure outside which is presumably atmospheric pressure. You should be able to improve on this by venting the container into another that is already below atmospheric pressure. Perhaps have a line of containers each venting into the next one in the chain with valves in between.

 

[BernieM]

Your assessment seems correct. For the pressures you are interested in, the ideal gas law would be adequate. Of course, integrity of the container would be an issue at those kinds of temperatures.

That's why I said that the container was an ideal container that could withstand any temperature (though no such critter exists) to avoid complications regarding the container.

In order for gas to escape, the pressure inside when hot must be greater than the pressure outside which is presumably atmospheric pressure. You should be able to improve on this by venting the container into another that is already below atmospheric pressure. Perhaps have a line of containers each venting into the next one in the chain with valves in between.

The outside of the container would be atmospheric pressure for the purposes of helping answer this question. But if I have a vacuum ultimately outside of the chamber, the inside of the chamber would eventually get to a vacuum also, and no longer exist at atmospheric pressure.

But I'm not yet seeing the answer I am looking for. So let me find another way to get this question posed:

Suppose I build an IEC device (Inertial Electrostatic Confinement), and instead of pumping it down with a vacuum pump, let the arc from my device heat a volume of hydrogen inside the container, which is at atmospheric pressure. Outside is also atmospheric pressure. Ignoring for now the valve and container, as I heat the hydrogen it expands, and gas escapes. The atoms per cubic volume is now reduced so I have the equivalent of a vacuum. Ultimately the internal pressure should always stay at atmospheric pressure and not go to a true vacuum when it's heated up. Only when allowed to cool would it become a vacuum.

I am fairly sure the gas laws would predict for lower pressures, but as the temperature gets extremely high (say 50 million to 200 million kelvins), does the process stop at some point or does the gas law no longer become reliable to calculate the conditions requiring that I use some other formula?

I think it comes down to 'at very high temperatures in millions of kelvinis, at a given non-zero pressure, what is the free mean path between atoms in the plasma'

Is there a limit (other than how hot I can heat the hydrogen, the container or the valve design) and what would those limits be caused by? Would it be a relativistic limit at one point where protons or nucleons are bouncing around at near C, for example?