Kinetic Theory of Gases: Effusion and Collisions

In summary, the conversation revolves around a concern with pages 1 and 2 of a link related to physical chemistry. The inconsistency in the author's use of notations \upsilon, \theta, and \phi is discussed, with the only angle shown in the diagram being \upsilon. The volume of the parallelepiped and the # of molecules crossing through dA in time dt involve \upsilon and \theta, respectively, but the flux again involves \upsilon. The conversation also includes the discovery of a legitimate error in the distribution and average flux calculations, which is later resolved.
  • #1
xatu
26
0
Question:

In the following link I'm concerned with only pages 1 and 2. I'm wondering if there is a typo or an error of some kind. I feel like there is some inconsistency to what the author refers to as [itex]\upsilon[/itex], [itex]\theta[/itex], and [itex]\phi[/itex]. The only angle shown in the diagram is [itex]\upsilon[/itex], which is the angle the constructed parallelepiped makes with the surface normal.

For instance, the volume of the parallelepiped involves [itex]\upsilon[/itex] and the # of molecules crossing through dA in time dt involves [itex]\theta[/itex], but then the flux again involves [itex]\upsilon[/itex]. Shouldn't all of those quantities involve only [itex]\upsilon[/itex]?

http://ocw.mit.edu/courses/chemistr...y-ii-spring-2008/lecture-notes/29_562ln08.pdf

Hopefully I am wrong. Thanks in advance for any help guys.
 
Physics news on Phys.org
  • #2
xatu said:
The only angle shown in the diagram is [itex]\upsilon[/itex], which is the angle the constructed parallelepiped makes with the surface normal.
It's not [itex]\upsilon[/itex], it's a somewhat stylised [itex]\theta[/itex]. Does that resolve it?
 
  • #3
Wow, I feel horrendously stupid. Sorry for wasting your time, haruspex.
 
  • #4
However, I did stumble across a legitimate error. The distribution, as well as the average flux, should contain [itex]e^{\frac{-mv^{2}}{2kT}}[/itex]. What is shown is [itex]e^{\frac{-mv^{2}}{kT}}[/itex] - missing the factor of 2 in the dominator of fractional exponent. However, the correct answer is shown for the result of the integral. Still should have that factor of 2 though.
 
  • #5
xatu said:
Wow, I feel horrendously stupid. Sorry for wasting your time, haruspex.
If it allows you to progress, my time was not wasted.:cool:
 

1. What is the Kinetic Theory of Gases?

The Kinetic Theory of Gases is a scientific model that explains the behavior of gases at the molecular level. It states that gases are made up of tiny, constantly moving particles that collide with each other and the walls of their container. This theory helps us understand properties of gases such as pressure, temperature, and volume.

2. What is effusion in the context of the Kinetic Theory of Gases?

Effusion is the process by which gas particles escape through a small opening or pore in a container. According to the Kinetic Theory of Gases, gas particles are constantly moving and have different speeds. As a result, some particles will have enough energy to escape through the opening while others will not. This process is important in understanding gas diffusion and the rate at which gases mix with each other.

3. How do collisions between gas particles affect pressure?

Collisions between gas particles are the main cause of pressure in a gas. When gas particles collide with each other or with the walls of their container, they exert a force. The more collisions that occur, the higher the pressure will be. This is why increasing the temperature or number of gas particles in a container will also increase the pressure.

4. How is temperature related to the average kinetic energy of gas particles?

According to the Kinetic Theory of Gases, the average kinetic energy of gas particles is directly proportional to the temperature of the gas. This means that as temperature increases, so does the average kinetic energy of the particles. This is because higher temperatures cause the particles to move faster, resulting in more frequent and energetic collisions.

5. How does the Kinetic Theory of Gases explain the behavior of ideal gases?

The Kinetic Theory of Gases is the basis for the ideal gas law, which describes the relationship between pressure, volume, temperature, and number of moles in an ideal gas. According to this theory, ideal gases have particles that are point masses with no volume, they do not experience intermolecular forces, and collisions between particles are perfectly elastic. While no gas is truly ideal, this theory helps us understand and make predictions about the behavior of gases under different conditions.

Similar threads

B Collision time interval of a gas molecule with wall of container
    • Thermodynamics
Replies
6
Views
1K
I Is GHG Theory/GW in conflict with Kinetic Theory of Gases?
    • Thermodynamics
Replies
6
Views
1K
Can gas kinetic theory explain heat transfer from gas to a container?
    • Thermodynamics
Replies
6
Views
1K
Assumptions in the derivation of the kinetic theory of gases
    • Mechanics
Replies
1
Views
1K
Kinetic theory of gases and velocity correlations
    • Mechanics
Replies
27
Views
14K
I Correlation between Symmetry number & Total wavefunction
    • Quantum Physics
Replies
9
Views
969
Kinetic Theory and Elastic Collisions
    • Introductory Physics Homework Help
Replies
5
Views
7K
Inelastic collision Two angles and final velocities
    • Introductory Physics Homework Help
Replies
3
Views
2K
Kinetic theory of gases: rebound speed and force questions
    • Mechanics
Replies
2
Views
2K
(2/3) as constant factor In Kinetic theory of gases
    • Mechanics
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top