Planck   Distribution

F[ν_, T_]:= ((8π h (ν^3))/(c^3)) (1/(Exp[((h ν)/(k T ))] -1))

c=  3  (10^10);  h= 6.6 (10^(-27));  k = 1.38  (10^(-16))

(1)   At the temperature of the present-day universe,   T= 3 K

Plot[F[(10^8)*ν, 3]*(10^24), {ν,1, 10000}]

λ =  (c/2000) (10^(-8))

The wavelength  =  0.15  cm  
 (Cosmic microwave background radiation)

(2)  At zero Celsius   (K=273)

Plot[F[(10^10)*ν, 273]*(10^18), {ν,1, 8000}]

λ =  N[(c/1800) (10^(-10))]

The wavelength  =  0.0017  cm      :   Infrared
Cannot see the light

(3)  At  Celsius   0,200, 500

Plot[{F[(10^10)*ν, 273]*(10^18),F[(10^10)*ν, 473]*(10^18),F[(10^10)*ν, 773]*(10^18) },   {ν,1, 10000}]

λ =  N[(c/5000) (10^(-10))]

The wavelength  =  0.0006  cm      :   Still in the  Infrared

(4)  At  Celsius  1000, 1500

Plot[{F[(10^11)*ν, 1773]*(10^17),F[(10^11)*ν, 1273]*(10^17) },   {ν,1, 5000}]

λ =  N[(c/1000) (10^(-11))]

At the end of the spectrum  ν= 4000 (1/sec) the visible light (8000 A)
starts to enter.

(5)  At  the sun's   surface  temperature  T=6000

Plot[F[(10^12)*ν, 6000]*(10^14),   {ν,1, 2000}]

λ =  N[(c/400) (10^(-12))]

Visible (red)  light
N.B.    Sun is not a black body

(6)  At   T=10000

Plot[F[(10^12)*ν, 10000]*(10^14),   {ν,1, 3000}]

λ =  N[(c/700) (10^(-12))]

Visible   violet  color

(7)  Temperature dependence

Plot[{F[(10^10)*ν, 273]*(10^17),F[(10^10)*ν, 473]*(10^17),F[(10^10)*ν, 773]*(10^17),F[(10^10)*ν, 1073]*(10^17),F[(10^10)*ν, 1273]*(10^17),F[(10^10)*ν, 1573]*(10^17),F[(10^10)*ν, 1773]*(10^17) },   {ν,1, 25000}, PlotRange->{0,50}]

As  T  increases    the maximum of the spectum shift towards    larger   ν  (shorter 
wavelengths)

As  T  increases    the region  where  R-J formula  is  valid   increases

(8)  Temperature    of    household    oven

Lemmon Meringue Pie                 220 C
Strawberry  Choux Crown            220 C 
Fesa di tacchino                           200 C
Stinco di Vitello ai porri     180 C

Conclusione:  per vedere se  le  patatine  (o la torta) sono  bruciate, il forno di casa
ha bisogno della lucina interna.