Black body radiation and elementary Earth’s thermodynamics

Version 0.1

Content

1        From black body concept to Planck’s law of radiation  2

1.1        Introduction 2

1.1.1        Nomenclature 2

1.1.2        The black body concept 3

1.1.3        Stefan-Boltzmann’s law 4

1.1.4        Lambertian emission and Stefan-Boltzmann radiance 4

1.1.5        Wien’s displacement law 5

1.1.6        Wien’s distribution law 6

1.2        Rayleigh-Jeans law of radiation 7

1.2.1        Stationary waves in the cavity  7

1.2.2        Counting the cavity modes 9

1.2.3        The volumetric energy spectral density of the cavity  10

1.2.4        Comparison with the Wien’s distribution law  10

1.3        Planck’s law of radiation  12

1.3.1        The energy quantization assumption  12

1.3.2        The frequency proportionality assumption  13

1.3.3        Wien’s displacement law in frequency and wavelength  15

1.3.4        The Stefan-Boltzmann law and the measurable radiated power  17

2        Elementary Earth’s thermodynamics  18

2.1.1        Black body thermal equilibrium  18

2.1.2        An elementary greenhouse effect formulation  19

3        References 20

Abstract

The concept of black body and the wavelength distribution of the emitted electromagnetic radiation as a function of the body temperature are the first steps to study and understand Earth’s thermodynamics and climate issues.

Keywords

Black body

BlackBodyV0-1