siewwen169 - 15-7-2005 at 03:53
hello,i have some question to ask here.
1. which of the following is not correct for
an ideal gas?
A. the average kinetic energy of the gas
increases with temperature
B. the force of repulsion between
molecules is proportional to the
distance between them
C. the gas molecules have mass but
negligible volume.
D. there are intermolecular forces
between molecules
my answer is D,but the answer given is B,why???
neutrino - 15-7-2005 at 06:16
They're both wrong. There are no forces in an ideal gas.
chemoleo - 15-7-2005 at 06:24
B is wrong becuase the force is INVERSELY proportional times the power to something, so the force of repulsion if you like decreases over the
molecular distance, while B says that the repulsion increases as distance does. Which is bollocks obviously.
The van der Waals repulsion increases something like 1/(r^6) , if I remember correctly.
[Edited on 15-7-2005 by chemoleo]
unionised - 17-7-2005 at 01:46
Neutrino is right. Both B and D are wrong. The R^-6 law is nothing to do with an ideal gas.
You could argue that B is correct, provided that the constant of proportionallity is zero; but that's stupid. Someone cocked up when setting the
question.
12AX7 - 17-7-2005 at 06:15
If nothing else, B is "more" wrong and thus the answer.
But guys, D must be true since molecules collide and bound off each other!
Tim
neutrino - 17-7-2005 at 06:22
I agree, B seems to be more wrong. D is still wrong because one of the basic tenets of an ideal gas is that there are no intermolecular forces.
Quibbler - 27-7-2005 at 06:02
Repulsive forces are often approximated to r^-12. It's the attractive forces that are proportional to r^-6. But B and D are both very wrong.
I'm not really sure about C either - is mass important? I think it's just the number of molecules, though they are assumed to have zero
volume.
unionised - 27-7-2005 at 09:58
They need mass to carry kinetic energy and momentum. Without these you don't have a temperature and pressure.
"But guys, D must be true since molecules collide and bound off each other! "
If they have no volume they have no area so they cannot collide. I think there may be more than one definition of ideal gas.
[Edited on 27-7-2005 by unionised]
Quibbler - 28-7-2005 at 10:07
That's an interesting point you make. I think ideal gas molecules are assumed not to collide with each other, or at least these collisions are
very much less frequent than those with the container walls. Yes mass is needed to give the kinetic energy meaning, but niether pressure or volume
depend on the mass of the atoms in an ideal gas. Billiard balls bounce off each other with the only force being due to momentum changes.
[Edited on 28-7-2005 by Quibbler]
neutrino - 28-7-2005 at 16:51
Actually, one of the tenets of kinetic molecular theory is rapid, elastic molecular collisions. That's strange, given their lack of volume and
forces.
epck - 29-7-2005 at 13:43
The kinetic theory of gases will give rise to the ideal gas law in the diffuse limit. In other words the density of the gas is so low the probability
of the molecules interacting is negligible.
Here's another way to the ideal gas. Consider a box of length L filled with non-interacting particles of mass, m. While inside the box the
particles have the following Hamiltonian, H=p^2/2m for 0 < x,y,z < L. For the particle in a box we get the following well known result from the
Schrodinger eqn:
E_(nx,ny,nz)=h^2(nx^2+ny^2+nz^2)/8mL^2
When we take the high temperature limit, ie. the gap between the energy levels is very small, the following form for the translational partition
function, q, is obtained:
q=V*(2*pi*mkT/h^2)^1.5
Now using the eqn for the pressure p=kT(dln(Q)/dV) where Q=q^N/N! we get the ideal gas law,
p=NkT/V.
Notice in our original Hamiltonian, H=p^2/2m, we assumed the potential inside the box was zero so the particles do not interact with each other.
Quibbler - 1-8-2005 at 04:33
I think this may be a circular argument. In order to get rid of the Lagrange multiplier beta (B) the ideal gas equation is assumed to hold to give
B=1/kT.
Statistical thermodynamics is a minefield