Questions on Kinetic Theory of Gases

[ananthu]

I have some questions on kinetic theory of gases:

kinetic theory assumes that the inter molecular force of attraction between two molecules of a gas is negligible. This assumption applies to the condition that the said gas is either at low pressure or at high temperature. This means, when the gas is at low pressure, the molecules will be far apart and therefore the IMF is negligible. Or,also when at high temperature they will be far apart and same is true.
But the following thing is not clear to me. When the temperature is high, the velocities of the molecules will be also be high and this should result in more number of collisions which will other wise increase the pressure. that is, when the temperature is high the pressure should be also high.

 

[Hootenanny]

Essentially, the kinetic theory of gases boils down to the assumption that the pressure is result of the collisions between molecules and ignores the contributions from the IMF. At higher temperatures, the kinetic energy of the molecules will be much higher than the potential energy between the molecules. Thus, the IMF can be neglected. At lower pressures the "average distance" between the molecules will be large & thus the IMF will be weaker.

 

[ananthu]

Thank you for the replly.
But my specific doubts were not answered.

My question is whether it is possible for a gas to exist simultaneously at higher temperature and at lower pressure or higher temperature and at higher pressure?

If so, how? In that case, how to deal with the IMF aspect? If anybody gives explanations with simple illustrations, it will be helpful to me.

 

[Hootenanny]

Thank you for the replly.
But my specific doubts were not answered.

My question is whether it is possible for a gas to exist simultaneously at higher temperature and at lower pressure or higher temperature and at higher pressure?

If so, how? In that case, how to deal with the IMF aspect? If anybody gives explanations with simple illustrations, it will be helpful to me.

The point regarding high/low pressures/temperatures is somewhat irrelevant here. The kinetic theory of gases does not assume that the gas is either at a low pressure nor at a high temperature. It merely assumes that the potential energy of the gas is negligible when compared with the kinetic energy of the gas.

Discussion of the corresponding pressures and temperatures is a somewhat misleading over simplification in order to "justify" these assumptions. Roughly, the postulates of kinetic theory can be found on the wiki page: http://en.wikipedia.org/wiki/Kinetic_theory . Note the absence of any reference to high/low pressures/temperatures.

Your question of the simultaneous existence of a gas with high temperature and low pressure is moot as it isn't relevant with how we deal with the IMF aspect, as you put it.

 

[Philip Wood]

"My question is whether it is possible for a gas to exist simultaneously at higher temperature and at lower pressure or higher temperature and at higher pressure?"

That part of your question seems to be answered by pV = nRT; it all depends what you do to V. If you increase V enough at the same time that you increase T, then P can fall, and so on.

This, of course, uses the ideal gas approximation, but in most circumstances the argument will work with real gases.

I've never felt it helpful to discuss the effects of IMFs in terms of gas pressure. It seems to me that it's much more useful to discuss them in terms of gas density.