Nebenrechnung zu Aufgabe 1.2 d)

c = 3*10^8; h = 6.626*10^-34;

D[a^3/(Exp[a/(k T)] - 1), a]

NSolve[
      0 == ((1.257614857964978`*^19 (a^3) (E^(1.257614857964978`*^19 a)))/(((-1 + (E^(1.257614857964978`*^19 a))))^2)) + ((3 (a^2))/(-1 + (E^(1.257614857964978`*^19 a)))), a]

k = 1.38*10^-23; T = 5762;

(1/15) (k^4) (π^4) (T^4)*2*π/c^2/h^3