Understanding Non-Interaction in Ideal Gases: Exploring Particle Collisions

[fluidistic]

Hi,
The particles of any ideal gas are said to non-interact between each other, however they experience collisions between themselves.
My question is : Hence what is the meaning of "non-interact"? Does this mean that the molecules don't change with time?
Thank you.

 

[Bob S]

In general, Van der Walls forces correct the "ideal gas law" for inter-molecular collisions. So "non-interact" applies to gases that obey the ideal gas law pv=nRT. But because of the difference between the heat capacity at constant volume and at constant pressure, "ideal gases" obey pv^g= nRT, where g =1.4 for air (diatomic), and 1.67 for monoatomic gases.

 

[Mapes]

In general, Van der Walls forces correct the "ideal gas law" for inter-molecular collisions. So "non-interact" applies to gases that obey the ideal gas law pv=nRT. But because of the difference between the heat capacity at constant volume and at constant pressure, "ideal gases" obey pv^g= nRT, where g =1.4 for air (diatomic), and 1.67 for monoatomic gases.

Bob, take another look at that last equation; it's not dimensionally correct, for one.

 

[Arjan82]

This post shouldn't be here...

 

[Arjan82]

In general, Van der Walls forces correct the "ideal gas law" for inter-molecular collisions. So "non-interact" applies to gases that obey the ideal gas law pv=nRT. But because of the difference between the heat capacity at constant volume and at constant pressure, "ideal gases" obey pv^g= nRT, where g =1.4 for air (diatomic), and 1.67 for monoatomic gases.

I think you are mistaking two different formula's here. There is the gas law [tex] p = \rho R T [/tex] and there is the Poisson's relation for isentropic flow: [tex] p = C \rho^{\gamma} [/tex] with [tex] \gamma [/tex] equal to your g and C a not known constant.

 

[Arjan82]

Hi,
The particles of any ideal gas are said to non-interact between each other, however they experience collisions between themselves.
My question is : Hence what is the meaning of "non-interact"? Does this mean that the molecules don't change with time?
Thank you.

A perfect or ideal gas is a gas in which:
(1) the distance between the individual molecules is so large (order of magnitude of 10d_o, with d_o the linear dimension of the molecule) that the intermolecular cohesive forces (e.g. van der waals forces) are extremely weak;
(2) the molecules travel independently of each other, except when colliding elastically once in a while (typical distance between collisions 200do);
(3) in addition to (1) the potential energy of a molecule within the force field of another molecule is much smaller than the kinetic energy of the molecule.

 

[Dadface]

Bobs equation is dimensionally correct but it refers to an adiabatic change(infinitely rapid with zero heat entering or leaving the gas).For an isothermal change(infinitely slow with zero temperature change)g=1.When we say that the molecules do not interact we are just making a simplifying assumption and ignoring the intermolecular forces.Other simplifying assumptions are made when deriving the ideal gas equation and the equation breaks down under those condition when the assumptions break down(e.g. as the pressure increases)As Bob suggested Van der Waals equation is an improvement taking into account the intermolecular forces.

 

[Mapes]

Bobs equation is dimensionally correct but it refers to an adiabatic change(infinitely rapid with zero heat entering or leaving the gas).

You're saying that the units Pa m^3(1.4) = Pa m^4.2, Pa m^3(1.67) = Pa m^5.01, and J are all equivalent?

 

[Dadface]

You're saying that the units Pa m^3(1.4) = Pa m^4.2, Pa m^3(1.67) = Pa m^5.01, and J are all equivalent?

Thank you Mapes for pointing out my error,the proper adiabatic equation is P*V to the power of g is a constant.I was having one of my dopey moments.

 

[fluidistic]

Thank you very much to all.
From

A perfect or ideal gas is a gas in which:
(1) the distance between the individual molecules is so large (order of magnitude of 10d_o, with d_o the linear dimension of the molecule) that the intermolecular cohesive forces (e.g. van der waals forces) are extremely weak;
(2) the molecules travel independently of each other, except when colliding elastically once in a while (typical distance between collisions 200do);
(3) in addition to (1) the potential energy of a molecule within the force field of another molecule is much smaller than the kinetic energy of the molecule.

, I think I get it better to what is an ideal gas.
I had this question since today because the professor introduced us what is an ideal gas roughly by saying that it's a gas in which the molecules don't interact. So I thought that at a given temperature all the molecules of an ideal gas would have the same kinetic energy (they could have a different one, but as there was no reason I supposed not), but my professor was using a formula involving an average kinetic energy of the molecules, confusing my mind. After this I read on wikipedia that in an ideal gas the molecules can collide, which totally confused me about the nature of ideal gases and so I asked the question here.