lecture_11_chex42

# lecture_11_chex42 - Kinetic Theory of Gases Kinetic Theory...

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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 &amp; 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 &amp; Statistics Review Probability &amp; 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 = = + + + + &gt;= &lt; 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 &amp; Statistics Review Probability &amp; Statistics Review ! The average value of x becomes = &gt;= &lt; 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 &amp; Statistics Review Probability &amp; 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, &lt;x&gt; is now given by...
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## This note was uploaded on 12/29/2011 for the course CHE 142 taught by Professor Ceweb during the Fall '09 term at UCSB.

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lecture_11_chex42 - Kinetic Theory of Gases Kinetic Theory...

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