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Plot the following functions with energy at different temperatures. a) Maxwell-Boltzmann distribution b) Fermi-Dirac distribution c) Bose-Einstein distribution , . - Scilab Solution

a) Maxwell-Boltzmann distribution

b) Fermi-Dirac distribution 

c) Bose-Einstein distribution



a) Maxwell-Boltzmann distribution

// Define the constants and energy range

mu = 0.0;

tempE1 = 0.1;

tempE2 = 0.5;

eps = [0.01:0.01:2]';


// Calculate the distribution functions

feps1 = exp(-(eps-mu)/tempE1);

feps2 = exp(-(eps-mu)/tempE2);


// Plot the distribution functions

clf();

plot2d(eps, feps1, style = 2);

plot2d(eps, feps2, style = 3);

xgrid();

xlabel("$\epsilon$", "fontsize", 5, "color", black);

ylabel("$f(\epsilon)$", "fontsize", 5);

title("Maxwell-Boltzmann distribution at different temperatures");


// Display a legend for the two curves

legend(["T = " + string(tempE1), "T = " + string(tempE2)], location = "northwest");


b) Fermi-Dirac distribution 


// Define the constants and energy range

mu = 2.0;

tempE1 = 0.1;

tempE2 = 0.5;

eps = [0.01:0.01:6]';


// Calculate the distribution functions

feps1 = 1.0./(exp((eps-mu)/tempE1) + 1.0);

feps2 = 1.0./(exp((eps-mu)/tempE2) + 1.0);


// Plot the distribution functions

clf();

plot2d(eps, feps1, style = -7);

plot2d(eps, feps2, style = -9);

xgrid();

xlabel("$\epsilon$", "fontsize", 5, "color", black);

ylabel("$f(\epsilon)$", "fontsize", 5);

title("Fermi-Dirac distribution at different temperatures");


// Display a legend for the two curves

legend(["T = " + string(tempE1), "T = " + string(tempE2)], location = "northeast");


c) Bose-Einstein distribution


mu = 2.0;

tempE1 = 0.1;

tempE2 = 0.5;

eps = [0.01:0.01:4.2]';


feps1 = 1.0./(exp((eps-mu)/tempE1)+1.0);

feps2 = 1.0./(exp((eps-mu)/tempE2)+1.0);


plot2d(eps,[feps1],2,rect=[0,0,4,2])

plot2d(eps,[feps2],3,rect=[0,0,4,2])


xlabel("$\epsilon$", "fontsize", 5, "color", "black");

ylabel("$f(\epsilon)$", "fontsize", 5);

title("Bose-Einstein distribution at different temperatures");


legend(["T = " + string(tempE1); "T = " + string(tempE2)], location = "northeast");




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