Schwarzkörperstrahlung

Initialisierung

h = 6.626068×(10^(-34));
ℏ=(h/(2π));
k =1.3806503 (10^(-23));
e=1.60217646*(10^(-19));
c =299792458;
THz=(10^12);GHz=(10^9);MHz=(10^6);
nm=(10^(-9));

SetOptions[Plot,Frame->True,BaseStyle->{FontFamily->"Helvetica",16}];

Plots

Energiedichte vs. Frequenz

uωPlanck[ω_,T_]:=((ω^2)/((π^2)(c^3)))((ℏ ω)/((E^((ℏ ω)/(k T)))-1));
uωWien[ω_,T_]:=((ω^2)/((π^2)(c^3)))((ℏ ω)/(E^((ℏ ω)/(k T))));
ωMax[T_]:=2.8214 ((k T)/h)2π;
TωMax[ω_]:=ω(((2.8214 (k/h)2π))^(-1));
uωRJ[ω_,T_]:=((ω^2)/((π^2)(c^3)))k T;

νmax=2500;

Manipulate[Block[{$PerformanceGoal="Quality"},Show[{Plot[uωPlanck[ν 2π THz,T],{ν,0,νmax},ImageSize->400,FrameLabel->{"Frequenz ν [THz]",""},PlotStyle->{Thick,Blue},PlotRange->{0,0.5 (10^(-15))}],
Plot[uωWien[ν 2π THz,T],{ν,0,νmax},ImageSize->400,FrameLabel->{"Frequenz ν [THz]",""},PlotStyle->{Dashed,Red},PlotRange->{0,0.5 (10^(-15))}],
Plot[uωPlanck[ν 2π THz,TωMax[ν 2π THz]],{ν,0,νmax},ImageSize->400,PlotStyle->{Thin,Dashed,Gray},PlotRange->{0,0.5 (10^(-15))}],
Plot[uωRJ[ν 2π THz,T],{ν,0,νmax},ImageSize->400,PlotStyle->{Thin,Dashed,Blue}],Graphics[{Red,Disk[{ωMax[T]/(2π) /THz,uωPlanck[ωMax[T],T]},{νmax/100,1 (10^(-17))}]}]}]],{T,0.01,7000,ControlType->Slider,Appearance->"Labeled"},LabelStyle->Large]

Energiedichte vs. Wellenlänge

uλPlanck[λ_,T_]:=((8π h c)/(λ^5))(1/((E^((h c)/(λ k T)))-1));
uλWien[λ_,T_]:=((8π h c)/(λ^5))(1/(E^((h c)/(λ k T))));
λMax[T_]:=(1/4.96511) ((h c)/(k T));
TλMax[λ_]:=(1/4.96511) ((h c)/(k λ ));
uλRJ[λ_,T_]:=((8π h c)/(λ^5))(1/((h c)/(λ k T)));

λmax=4000;
plotRange=Automatic;
plotRange={0.0,0.3 (10^7)};

Manipulate[Show[{Plot[uλPlanck[λ nm,T],{λ,0,λmax},ImageSize->400,FrameLabel->{"Wellenlänge λ [nm]",""},PlotStyle->{Thick,Blue},PlotRange->plotRange,FrameTicks->{Automatic,None},ColorFunction->(ColorData["VisibleSpectrum"][#]&),ColorFunctionScaling->False,Filling->Axis,Epilog->Inset[Text[Style["(Subscript[λ, max])="<>ToString[N[FromDigits[RealDigits[λMax[T]*(10^9),10,5]]],InputForm,NumberMarks->False]<>" nm",24,FontFamily->"Helvetica"]],Scaled[{0.4,0.8}],{Left,Top}]],
Plot[uλPlanck[λ nm,TλMax[λ nm]],{λ,0,λmax},ImageSize->400,PlotStyle->{Thin,Dashed,Gray},PlotRange->plotRange],
Plot[uλWien[λ nm,T],{λ,0,λmax},ImageSize->400,PlotStyle->{Thin,Dashed,Red},PlotRange->plotRange],
Plot[uλRJ[λ nm,T],{λ,0,λmax},ImageSize->400,PlotStyle->{Thin,Dashed,Blue},PlotRange->plotRange]}],{T,10,7000,ControlType->Slider,Appearance->"Labeled"},LabelStyle->Large]