Physical Chemistry- Maxwell Boltzmann Distribution

In summary, the Maxwell Boltzmann distribution is a fundamental concept in physical chemistry that describes the average distribution of speeds or energies of particles in a system. It is closely related to the Boltzmann distribution, but only considers the kinetic energy of particles. The shape of the distribution is affected by factors such as temperature, mass, and type of gas or liquid. While it has been validated by experiments and is commonly used in real-world systems, it is based on certain assumptions and may not accurately predict the behavior of all systems.
  • #1
sdoyle1
23
0

Homework Statement



Use the maxwell Boltzmann distribution to derive an expression for <v^3>

Homework Equations


<v>=(8RT/piM)^1/2


The Attempt at a Solution


I know that you have to integrate from 0 to infinity v^3p(v)dv.. but I don't really know how to integrate this. I just need to find a general integral then I can look it up in the handbook for chemistry and physics...
 
Physics news on Phys.org
  • #2
Use the substitution u=v2 (maybe throw in the constants while you're at it), and you'll have an integral in the form of the gamma function.
 

1. What is the Maxwell Boltzmann distribution?

The Maxwell Boltzmann distribution is a mathematical representation of the probability of energy distribution among particles in a gas or liquid at a given temperature. It describes the average distribution of speeds or energies of particles in a system.

2. How is the Maxwell Boltzmann distribution related to physical chemistry?

The Maxwell Boltzmann distribution is a fundamental concept in physical chemistry as it helps us understand the behavior of particles in a system. It is used to predict the properties of gases, such as pressure, temperature, and volume, and to calculate thermodynamic quantities such as entropy and internal energy.

3. What factors affect the shape of the Maxwell Boltzmann distribution?

The shape of the Maxwell Boltzmann distribution is affected by several factors, including temperature, mass of particles, and the type of gas or liquid. As temperature increases, the distribution curve flattens and shifts towards higher energies, and particles with lower masses have higher average speeds.

4. How is the Maxwell Boltzmann distribution different from the Boltzmann distribution?

The Maxwell Boltzmann distribution is a special case of the Boltzmann distribution, which is a more general concept that applies to all systems, not just gases or liquids. The Maxwell Boltzmann distribution only considers the kinetic energy of particles, while the Boltzmann distribution takes into account both kinetic and potential energies.

5. Can the Maxwell Boltzmann distribution be applied to real-world systems?

Yes, the Maxwell Boltzmann distribution has been validated by experiments and is commonly used to describe the behavior of particles in gases and liquids. However, it is based on several assumptions, such as the particles being in thermal equilibrium and obeying classical mechanics, so it may not accurately predict the behavior of all systems.

Similar threads

Replies
6
Views
803
  • Electromagnetism
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Atomic and Condensed Matter
Replies
7
Views
2K
Replies
4
Views
3K
Replies
1
Views
903
Replies
17
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
Replies
4
Views
3K
Back
Top