/* Symbolic checks for Statistical Mechanics Unit I.
   Run: maxima --very-quiet -b classical-statistics.mac */
kill(all)$
display2d:false$

assume(a>0)$
f(v) := 4/sqrt(%pi)*a^(3/2)*v^2*exp(-a*v^2)$
normalization : integrate(f(v),v,0,inf)$
print("Maxwell-speed normalization residual =",
      ratsimp(normalization-1))$

vmp : 1/sqrt(a)$
print("Maxwell most-probable-speed residual =",
      radcan(subst(vmp,v,diff(log(f(v)),v))))$

z1 : C*beta^(-3/2)$
print("ideal-gas energy residual =",
      ratsimp(-N*diff(log(z1),beta)-3*N/(2*beta)))$

gaussian_q : sqrt(%pi/(beta*c))$
equipartition :
  -diff(log(gaussian_q),beta)$
print("equipartition residual =",
      ratsimp(equipartition-1/(2*beta)))$

Sst : N*kB*(log(V/N*(2*%pi*m*kB*T/h^2)^(3/2))+5/2)$
print("Sackur-Tetrode extensivity residual =",
      ratsimp(subst([V=q*V,N=q*N],Sst)-q*Sst))$

quit()$