Maxwell Distribution - THE MAXWELL-BOLTZMANN DISTRIBUTION...

Info icon This preview shows page 1. Sign up to view the full content.

THE MAXWELL-BOLTZMANN DISTRIBUTION CHEMISTRY 213 The molecular description of the bulk properties of a gas depends upon our knowing the mathematical form of the velocity distribution; That is, the probability, F ( v x , v y , v z ) v x v y v z , of finding a molecule with velocity components in the range v x to v x + ∆ v x , v y to v y + ∆ v y , and v z to v z + ∆ v z (see the last handout). This can be found by making two very simple assumptions: 1. The three components of the velocity are independent of each other. This implies that the velocity probability density can be written as: F ( v x , v y , v x ) = f ( v x ) f ( v y ) f ( v z ) (1) 2. All directions are equivalent (space is isotropic). This implies that the probability of find- ing a molecule moving with a certain velocity cannot depend on the direction; it is equally probable to find a molecule with any speed v moving in any direction. Mathematically, this implies that the probability density can only depend on the magnitude of the velocity, or the molecular speed. Hence, F ( v x , v y , v x ) = F ([ v 2 x + v 2 y + v 2 z ] 1/2 ). (2) By comparing Eqs. (1) and (2), we have f ( v x ) f ( v y ) f ( v z ) = F
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern