MATLAB: AN INTRODUCTION WITH APPLICATIO
MATLAB: AN INTRODUCTION WITH APPLICATIO
6th Edition
ISBN: 9781119626596
Author: GILAT
Publisher: WILEY
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Chapter 10, Problem 11P

Molecules of a gas in a container are moving around at different speeds. Maxwell’s speed distribution law gives the probability distribution P( v) as a function of temperature and speed:

P ( v ) = 4 π M 2 π R T 3 / 2 v 2 e M v 2 / 2 R T

Where M is the molar mass of the gas in kg/mol, R = 8.31J/(mol K), is the gas constant, T is the temperature in kelvins, and v is the molecule’s speed in m/s. Make a 3-D plot of P(v) as a function of i and T for 0 v 1 , 000 m/s and 70 T 320 K for oxygen (molar mass 0.032 kg/mol).

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A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at the z=0 plane as below. Both mediums are general, characterized by ( ε i, Mi, Ơi ). tot = [ ει μη σ] [ε, μη σε ] Ex Ex tot E₁₂ (z) = Ee Ex z=0 From conservation of energy: P₁AV'(z=0) + Piav'(z=0) = P2av²(z=0). Using the above show for lossless media that: ( 1 - ||²) = (1/M2 )|T|² .
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