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// Theory and Problems of Thermodynamics
// Chapter 11
// Kinetic Theory of Gases
// Example 7
clear ;clc;
//Given data
V1 = 1 // X-component velocity low range
V2 = 1.6 // X-component velocity upper range
// Caluclations
// Required fraction from The Maxwell-Boltzmann distribution of the X-component // velocity
// F = (1/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6)
// F = 1/2*((2/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6) - (2/sqrt(%pi))integrate// (exp(-X^2),'X',0,1))
F = erf(V2) - (2/sqrt(%pi))*V2*exp(-V2^2) - erf(V1) + (2/sqrt(%pi))*exp(-V1)
// Output results
mprintf('The fraction of molecules of a gas with speed between Vmp and 1.6Vmp = %4.4f', F)
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