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Graphing the Planck Function

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Graphing the Planck Function 

Problem

 

Data

 

 

Useful Equation

 

Planck Function

4.99320*10^19*Pi*h*nu^3/(c^3*exp(h*nu/(k*T))-1) 

``

 

Solution

 

Load the Plots package.

with(plots)

NULL

Planck's radiation formula in eV.

u := (0.62415e19*8)*Pi*h*nu^3/(c^3*exp(h*nu/(k*T))-1)

0.3308494320e-13*Pi*nu^3/(0.2694603599e26*exp(0.4797972484e-10*nu/T)-1)

(4.1)

NULL

Define constants.

``

Display the function in decimal form.

evalf(u)

0.1039394145e-12*nu^3/(0.2694603599e26*exp(0.4797972484e-10*nu/T)-1.)

(4.2)

NULLNULL

NULLNULL

Reset Variable.

T := 'T'

T

(4.3)

NULL

Generate function u for different values of T.

for q from 2 to 7 do u.q := subs(T = 1000*q, u) end do

0.3308494320e-13*Pi*nu^3/(0.2694603599e26*exp(0.2398986242e-13*nu)-1)

(4.4)

NULL

aa := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(2.398986242*10^(-14)*nu)-1)], nu = 0 .. 20*10^14, color = red)

NULL

 

bb := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(1.599324161*10^(-14)*nu)-1)], nu = 0 .. 20*10^14, color = orange)

 

 

cc := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(1.199493121*10^(-14)*nu)-1)], nu = 0 .. 20*10^14, color = yellow)

 

 

dd := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(9.595944968*10^(-15)*nu)-1)], nu = 0 .. 20*10^14, color = green)

NULL

NULL

ee := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(7.996620807*10^(-15)*nu)-1)], nu = 0 .. 20*10^14, color = blue)

NULL

NULL

ff := plot([3.308494320*10^(-14)*Pi*nu^3/(2.694603599*10^25*exp(6.854246406*10^(-15)*nu)-1)], nu = 0 .. 20*10^14, color = purple, title = "Energy Distribution Plots for T=2000 K-16,000 K")

 

display([aa, bb, cc, dd, ee, ff])

 

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