lecture_11_chex42

lecture_11_chex42 - Kinetic Theory of Gases Kinetic Theory...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Kinetic Theory of Gases Kinetic Theory of Gases Kinetic Theory: Theory that deals with prediction of transport ( , , D) and thermodynamic properties of gases based on statistical (average) description of the translational motion of its components (atoms & molecules). statistical description velocity distribution function kT mv / e kT m v ) v ( F 2 2 3 2 2 2 4 = Maxwell-Boltzmann speed distribution Probability & Statistics Review Probability & Statistics Review ! Suppose we have a series of observation for a value x which can take on a discrete set of values {x 1 , x 2 , x 3 ,x m } ! Suppose that in a series of N measurements we observe that x 1 occurs N 1 times x 2 occurs N 2 times : : : x m occurs N m times x 1 x 2 x 3 x 4 x m N ! Average value of x = = + + + + >= < m i i i m m x N N N x N ...... x N x N x N x 1 3 3 2 2 1 1 Probability & Statistics Review Probability & Statistics Review ! The average value of x becomes = >= < m i i i x P x 1 ! Define the probability that x i will be observed as P i 1 1 1 1 = = = = = m i i m i i i i N N P note N N P ! Now suppose that x (outcome of an experiment) can take on not discrete but continuous set of values ! Everytime that outcome of the experiment is between x and x+ x we add 1 to that bin xx+ x ! N(x) is the number of outcomes out of N total that is between x and x+ x Probability & Statistics Review Probability & Statistics Review ! The value P(x) is proportional to the length of segment x. We define probability density function f(x) such that P(x)=f(x) x ! Thus, the probability that an experimental outcome will be between x and x+ x is N ) x ( N ) x ( P = ! The average value of x, <x> is now given by...
View Full Document

This note was uploaded on 12/29/2011 for the course CHE 142 taught by Professor Ceweb during the Fall '09 term at UCSB.

Page1 / 15

lecture_11_chex42 - Kinetic Theory of Gases Kinetic Theory...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online