The Paradox of Gas Density: Why Is the Center Not Higher?

In summary, the blue line crosses the center of the container more often than the red line. But this doesn't mean that the density (and pressure) of the gas at the center is higher than that near the sides.
  • #1
ramollari
437
1
Suppose you have an ideal gas in a closed container. The gas molecules will be moving at random at very high speeds.
Now I've figured out that the probability of a gas molecule for being in the center of the container is higher than the probability of being near the sides. Then should we also conclude that the density (and pressure) of the gas at the center is higher than that near the sides? This conclusion doesn't seem to hold.
 
Physics news on Phys.org
  • #2
How's the probability of a particle being near the center higher?
If the probability density of a particle's position is uniform, then you'd have more chance of finding it near the sides, since the volume of a region with the sides as an outer boundary is generally much larger than a volume that is kept near the center. This doesn't affect the density, though.
 
  • #3
Take the particle isolated. If it is hit by other particles, then it has more probability to be found near the centre.
Take a look at the following simulation with Brownian motion, by setting m1/m2 = 1. http://home.wanadoo.nl/perpetual/brownian.html The container area colours blue (particle's path) near the center much faster.
 
Last edited by a moderator:
  • #4
On a side note, the effects of gravity would lead to a particle overall being more likely to be found near the bottom of a standing container. Aside from that, I have not enough experience with physics probability to comment further.
 
  • #5
ramollari said:
Take the particle isolated. If it is hit by other particles, then it has more probability to be found near the centre.
Take a look at the following simulation with Brownian motion, by setting m1/m2 = 1. http://home.wanadoo.nl/perpetual/brownian.html The container area colours blue (particle's path) near the center much faster.
That's a nice link.

But it's not correct to say that the probability of finding a particle near the center is higher because the blue line crosses near the center more often. What you need to look at is the position of the red particle. It's presence in the box at any instance is equally likely to be anywhere.
Look at all the gray dots. They are uniformly distributed over the box too.
 
Last edited by a moderator:
  • #6
Galileo said:
That's a nice link.
Seems a bit cranky to me. :rolleyes:
But it's not correct to say that the probability of finding a particle near the center is higher because the blue line crosses near the center more often. What you need to look at is the position of the red particle. It's presence in the box at any instance is equally likely to be anywhere.
Look at all the gray dots. They are uniformly distributed over the box too.
Right. I think the animation was probably written to illustrate brownian motion and has several built-in assumptions which break down when you put m1/m2 = 1. If it were accurate, then for m1/m2 = 1, the red dot would move exactly like any other dot. But it doesn't. While the gray dots are uniformly distributed and move at some average speed, the red dot zooms all over the place. I don't think so.
 
  • #7
put n=200 and m1/m2 = 1.
 

1. What is the paradox of gas density?

The paradox of gas density refers to the fact that, in a container of gas, the molecules in the center of the container have the same density as those on the edges, even though one might expect the center to be more densely packed due to the weight of the molecules above it.

2. Why is the center of the gas not higher in density?

The reason for this paradox is due to the nature of gas molecules. Gas molecules are in constant motion and collide with each other and the walls of the container. This results in a uniform distribution of molecules throughout the container, rather than a higher density in the center.

3. How does pressure affect the paradox of gas density?

Pressure does not directly affect the paradox of gas density. However, an increase in pressure can lead to a decrease in volume, causing the gas molecules to be more densely packed. This can give the illusion of a higher density in the center, but in reality, the molecules are still evenly distributed throughout the container.

4. Can the paradox of gas density be observed in other states of matter?

Yes, the paradox of gas density can also be observed in liquids and solids. In liquids, the molecules are still in constant motion and can freely move around, resulting in a uniform distribution. In solids, the molecules are tightly packed and vibrate in place, maintaining a consistent density throughout the object.

5. How does temperature play a role in the paradox of gas density?

Temperature also does not directly affect the paradox of gas density. However, as the temperature increases, the molecules have more energy and move faster, resulting in a higher pressure and potentially a decrease in volume. This can give the appearance of a higher density in the center, but the molecules are still evenly distributed.

Similar threads

Fluid Forces in a Manometer: Understanding Pressure and Kinetic Energy
    • Introductory Physics Homework Help
Replies
2
Views
686
The van der Waals Equation: What is the exact meaning of 'volume of gas'?
    • Chemistry
Replies
5
Views
1K
I Ideal working gas for a Stirling engine
    • Thermodynamics
Replies
1
Views
1K
Ideal Gas Law - Adding additional gas & additional question
    • Other Physics Topics
Replies
4
Views
1K
Volumetric flow rate ratio calculation
    • Materials and Chemical Engineering
Replies
1
Views
438
Calculating temp change releasing a compressed gas
    • Other Physics Topics
Replies
5
Views
2K
B Why gas clouds collapse if the forces are conservative?
    • Other Physics Topics
Replies
15
Views
1K
Adiabatic gas cooling/heating: Explaining Conceptually
    • Other Physics Topics
Replies
2
Views
1K
Two gases separated by a piston
    • Introductory Physics Homework Help
Replies
6
Views
2K
A Why are the Navier-Stokes equations inconsistent in this case?
    • Classical Physics
Replies
18
Views
1K

Hot Threads

Recent Insights

Back
Top