Spektrales Emissionsvermögen des schwarzen Körpers. Abb. 1.4-7 Wedler, Physikalische Chemie

black_body.py

import matplotlib.pyplot as plt
import numpy as np
# rho   = 8 pi hc/(lambda^5 *(exp(hc/(lambda k T)))-1)
# x     = lambda k T /(h c)
# T     = x *(h c)/(lambda k)
# rho   = 8 pi hc/((h c)^5/(k T)^5 * x^5 *(exp(x)-1)
# rho   = (8 pi (k T)^5/(h c)^4)/ (x^5 *(exp(x)-1))
title_text = 'Black Body Radiation'
n_temps = 10
pi = np.pi
temperatures = np.linspace(800, 0.1, n_temps)
rho = np.vectorize(
    lambda w_length, t: 8 * pi * (6.626 * 10**-34) * (3 * 10**8) / (
        w_length**5 * (
            np.exp(
                (6.626 * 10**-34) * (3 * 10**8) / (w_length * 1.381 * 10**-23 * t)
            ) - 1
        )
    )
)

fig, ax = plt.subplots()
line1 = ax.plot()

x_max_min = [1e-16, 3 * 10**-5]
y_max_min = [0, 2 * 10**-3]

x_range = np.linspace(x_max_min[0], x_max_min[1], 200)

max_line_x = []
max_line_y = []

for temp in temperatures:
    line1, = ax.plot(
        x_range, rho(x_range, temp)
    )
    line1_y = line1.get_ydata()
    line1_x = line1.get_xdata()

    x_coord = line1_x[np.argmax(line1_y)]
    y_coord = max(line1_y)

    max_line_x.append(x_coord)
    max_line_y.append(y_coord)

    ax.annotate(
        str(temp), 
        xy=(x_coord, y_coord), 
        xytext=(x_coord, y_coord)
        )
ax.plot(max_line_x, max_line_y, '-.',  color='black')
ax.set_title('')
ax.set_xlabel(r'$\lambda, m$')
ax.set_ylabel(r'$\rho, J m^{-4}$')

plt.show()