## Related questions with answers

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:

$P ( v ) = 4 \pi \left( \frac { M } { 2 \pi R T } \right) ^ { 3 / 2 } v ^ { 2 } e ^ { \left( - M v ^ { 2 } \right) / ( 2 R 7 ) }$

where M is the molar mass of the gas in kg/mol, R = 8.31 J/(mol K), is the gas constant, Tis the temperature in kelvins, and vis the molecule's speed in m/s. Make a $3 - \mathrm { D }$ plot of $P ( v )$ as a function of $v$ and $T$ for $0 \leq v \leq 1000 \mathrm { m } / \mathrm { s }$ and $70 \leq T \leq 320 \mathrm { K }$ for oxygen (molar mass 0.032$\mathrm { kg } / \mathrm { mol } )$ .

Solution

VerifiedUse Matlab function "surf" to solve the given Problem.

clear; clc;

R = 8.31;
M = 0.032;
v = linspace(0,1000,28);
t = linspace(70,320,16);
[T, V] = meshgrid(t,v);
Z = 4*pi*(M./(2*pi*R*T)).^(3/2). V.^2.exp(-MV.^2./(2R*T));
surf(V,T,Z);
xlabel('Speed (m/s)')
ylabel('Temperature (K)')
zlabel('Probability')

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