Paresh:

A fundamental assumption of the ideal gas law is that the individual particles of the gas do not interact. That is, there are no interparticle forces, nor do they collide. This implies infinitely small particles. Basically, any gas at a low enough pressure and high enough temperature will behave very close to an ideal gas. For example, nitrogen (N2) at STP is a close approximation to an ideal gas. Helium at STP is an even better approximation, but still not perfect. In fact, no real physical gas behaves exactly as an ideal gas.

Any gas will deviate from the ideal gas law if 1) the pressure is increased, or 2) the temperature is lowered. The pressure, or temperature at which deviation from ideal gas law behavior depends on the particles of the gas. Nitrogen (N2), a small, neutral, low polarizability molecule and has very low intermolecular forces. This gives N2 a very low boiling point (about 77 Kelvins). At atmospheric pressure, you'll have to lower its temperature to close to it's boiling point before you see significant deviation from the gas law. However, if the pressure is increased, say to 100 or 1000 atm., N2 will deviate from ideal gas law behavior even at room temperature.

In a similar way, Helium will show the same behavior. Helium, however, is a very small particle (noble gas = atoms not molecules), is extremely non-polarizable, and has very low inter-atomic forces. This results in a very low boiling point, about 4 Kelvins. Thus, Helium will demonstrate ideal gas law behavior to temperatures much closer to its boiling point and to much higher pressures when compared to N2.

There's no sharp transition between ideal gas law behavior and non-ideal behavior. The change is gradual and, as mentioned, dependent on pressure AND temperature. As far as Helium is concerned, it just so happens that at atmospheric pressure, the deviation becomes significant and measureable (but not drastic) by about 50 Kelvins. That same degree of deviation would be observed at higher temperatures for higher pressure, lower temperatures for lower pressures. There's nothing special about 50 Kelvins with respect to Helium's deviation from ideal gas law behavior; it's just a matter of degree (no pun intended).

I hope this helps.

Paresh:

A fundamental assumption of the ideal gas law is that the individual particles of the gas do not interact. That is, there are no interparticle forces, nor do they collide. This implies infinitely small particles. Basically, any gas at a low enough pressure and high enough temperature will behave very close to an ideal gas. For example, nitrogen (N2) at STP is a close approximation to an ideal gas. Helium at STP is an even better approximation, but still not perfect. In fact, no real physical gas behaves exactly as an ideal gas.

Any gas will deviate from the ideal gas law if 1) the pressure is increased, or 2) the temperature is lowered. The pressure, or temperature at which deviation from ideal gas law behavior depends on the particles of the gas. Nitrogen (N2), a small, neutral, low polarizability molecule and has very low intermolecular forces. This gives N2 a very low boiling point (about 77 Kelvins). At atmospheric pressure, you'll have to lower its temperature to close to it's boiling point before you see significant deviation from the gas law. However, if the pressure is increased, say to 100 or 1000 atm., N2 will deviate from ideal gas law behavior even at room temperature.

In a similar way, Helium will show the same behavior. Helium, however, is a very small particle (noble gas = atoms not molecules), is extremely non-polarizable, and has very low inter-atomic forces. This results in a very low boiling point, about 4 Kelvins. Thus, Helium will demonstrate ideal gas law behavior to temperatures much closer to its boiling point and to much higher pressures when compared to N2.

There's no sharp transition between ideal gas law behavior and non-ideal behavior. The change is gradual and, as mentioned, dependent on pressure AND temperature. As far as Helium is concerned, it just so happens that at atmospheric pressure, the deviation becomes significant and measureable (but not drastic) by about 50 Kelvins. That same degree of deviation would be observed at higher temperatures for higher pressure, lower temperatures for lower pressures. There's nothing special about 50 Kelvins with respect to Helium's deviation from ideal gas law behavior; it's just a matter of degree (no pun intended).

I hope this helps.

43 K - the so-called inversion temperature for helium. Above this temperature, Не gas can not be liquefied or even cooled when passing through the choke. Its temperature will only rise by friction. Below the inversion temperature Van-der-Waals intermolecular forces become significant and if the gas expands, its temperature decreases. Inversion point separates the region where the gas can be considered as the ideal gas from a real gas field, where the intermolecular interactions are significant.

I recall that the main properties of an ideal gas: molecules - infinitesimal, interaction between molecules - absent, the only type of interaction - absolutely elastic collision. Van-der-Waals introduced two amendments:

1) an amendment to the inaccessible volume - a molecule has a volume and other molecules can occupy this place;

2) An amendment to the internal pressure - the molecules are attracted to each other, creating a pressure in addition to the vessel walls.

If I can add a hint, from the characteristics of an ideal gas, no 'ideal gaseS' exist. Only one species exist, 'THE ideal gas', where the species of the molecule –or whatsoever particle– is irrelevant.

Dear Franco, saying that exists only the ideal gas it is right. As the definition says it is only an idea. Obviously when you apply this idea to real system things are different. There are many quantities tat depends on species characteristics. But consider statistical mechanics. First of all the partition function contains the mass of the species and therefore all the thermodynamic quantities depending on it such as the entropy, depend on the mass. Moreover, internal structure of the species, both atomic and molecular have an internal structure. Even if neglecting the interparticle interaction this makes the difference between the species. Therefore the energy of a system of particles of the same species is given by the internal and cotributions. this affects also the isentropic coefficients. affecting the behaviors of a flowing gas.

An ideal gas is not a system of non-interacting particles, otherwise it could not be applyied to any real system, but of particle interacting only through collisions, i.e. the interaction time is much smaller than the time interval between two collisions.

Fundamentally, the real behaviors arise when this condition is not fulfilled anymore.

We have to remember that Van Der Waals did not know the quantum mechanics, and its definition of real gas is limited by the idea of actracting balls.

Now the definition of interaction have to pass through the interaction potential. The simplest interparticle potential is a well of a given depth and a repulsive branchat short range. However there are potentials with barriers, multiple wells and so on.

The depth of the well determine the inversion temperature, the derivative of the repulsive branch determine the hardness of the interaction.

The parameters of the Van Der Waals low for real gases does not depend on the temperature, while in real cases it depends on the temperature.

Good books are Landau, Lifshitz, Statistical Physics,

Chapman, Cowlings The mathematical theory of non-uniform gases

Is this matter has anything to do with Joule's law?

I would like to add a brief discussion about the inversion temperature in this context:

The inversion temperature corresponds the point at which the Joule-Thompson coefficient, μ, (the isenthalpic dT/dP) changes sign with for any given pressure. There are other ways to describe it, but this one will do for now. The inversion temperatures of a gas (there are normally two, one at low temperature and another at high temperature for a particular pressure) do not really indicate when the gas departs significantly from ideal behavior. Rather, it indicates where the real gas behaves most like an ideal gas. Confused? Read on!

I would argue a reasonable measure of ideality might rather be the gas's Joule-Thompson coefficient, μ, which is a function of both temperature and pressure. An ideal gas has a 0K inversion temperature because it's Joule-Thompson coefficient is zero everywhere. Hence, the ideal gas law does not predict the Joule-Thompson effect and ideal gasses do not exhibit the effect either. Helium, the most ideal of real gasses has μ = -0.060 K/atm at STP. Carbon dioxide, a pretty non-ideal gas, has μ = 1.1 K/atm at STP. Notice I've specified temperature AND pressure.

But a non-ideal gas can behave nearly like an ideal gas at a particular temperature and pressure where μ is nearly equal to zero, or about to change sign (hence, the term "inversion"). The plot of where μ changes sign forms an arc dividing the pressure-temperature plane. For all practical purposes, a real gas always remains non-ideal at all temperatures and pressures, regardless of which side of the inversion curve it's on.

On the other hand, a real gas behaves more ideally the closer to the inversion curve it gets (assuming one exists at that temperature or pressure). Why? Because that is the locus (T and P) where μ = 0 or near zero. So the inversion temperature is not some kind of dividing line between ideal and non-ideal behavior. The gas is non-ideal on either side of the inversion curve (where μ is significantly different from zero) and most ideal when closest to it (where μ is close to zero).

There's a good discussion about this in "Physical Chemistry" by Atkins and de Paula, 7th edition, 2002, (ISBN 0-7167-3539-3), Chapter 3, in the discussion of the temperature dependence of enthalpy. That's now an old text, but I've no doubt any other good physical chemistry textbook would have a similar discussion.

I hope this helps!