### Post by IBDaMann on Jun 3, 2019 16:08:10 GMT

*Black Body*Science*Black Body*science is a collection of physics models that share the common underlying definitions and relationships established by Max Planck and applied in Planck's Law

**Body**: Any delimited, contiguous collection of matter. Black Body science applies to all matter, always, everywhere, whether it is an individual atom or a planet with an atmosphere and a hydrosphere.

**Black Body**: Any body in which thermal activity is occurring. The modifier "black" simply implies a focus on the body's thermal properties, i.e. having associated thermal energy and thermally radiating that energy in the form of electromagnetic radiation. The Laws of Thermodynamics are hard-coded into the definition of a black body: 1) by establishing an equilibrium temperature T for each body absorbing thermal radiation from a source such that the body's temperature will rise until reaching T and then will achieve thermal equilibrium (remaining at temperature T) ensures adherence to the 1st law of thermodynamics and 2) ensures thermal energy flows from higher temperature to lower temperature.

**Temperature**: Absolute temperature, usually measured in Kelvins. Only matter has temperature because only matter has associated thermal energy. Increasing a body's thermal energy increases its temperature.

**Energy State**: Another term for temperature but focuses on the amount of thermal energy associated with a particular black body, i.e. its energy state. Increasing a body's thermal energy increases its energy state.

**Emissivity Constant**: A numerical coefficient strictly between 0.0 and 1.0 (0.0 and 1.0 are purely theoretical limits that do not exist in nature) representing the body's total thermal efficiency percentage to absorb and to emit thermal radiation over all combined wavelengths

**Boltzmann Constant**= 1.380649 × 10

^{−23}Joules/Kelvin = 1.38064852 ×10

^{−16}Ergs/Kelvin = 8.6173303 ×10

^{−5}Electron_Volts/Kelvin

**Stefan-Boltzmann Constant**= 5.67 × 10^−8 watts / meter^2 squared per kelvin^4

**Planck's Constant**= 6.62607004 × 10

^{-34}m

^{2}*kg /second. It is the "quantum," or "smallest amount possible" of electromagnetic activity. Planck's constant relates a photon's frequency to energy, which Einstein related to mass. In November of 2018, the

*General Conference on Weights and Measures*redefined the kilogram to be based on Planck's constant.

**c**= The speed of light in a vacuum = 299,792,458 meters per second

**Wavelength and Frequency**: All electromagnetic radiation occurs at the speed of light in the form of a sine wave.

*Frequency*and

*Wavelength*are inverses of each other so either one can be used to calculate the other. Ergo, the longer the wavelength the smaller the frequency and the greater the frequency the shorter the wavelength. Both terms are used in

*Black Body*science because each one has its intuitive applications, e.g. frequency is a factor in calculating the energy of a photon, wavelength makes radiation calculations easier, etc..

**Frequency**=

**c**/

**Wavelength**

**Wavelength**=

**c**/

**Frequency**

**Planck's Law**

Planck's law has three key aspects which should be examined in detail:

1. The quantization of energy and the 2nd law of thermodynamics

2. The determination of the energy of a photon,

3. The power emitted by a black body of a given temperature for a given wavelength

**1. Quantization of Energy and Photons**

Black body science is predicated on energy occurring in discrete units and is how Max Planck

__hard-coded the 2nd law of thermodynamics into the__. The idea is that black bodies have discrete energy states like the frets on a guitar. A body of a given energy state/temperature will emit a photon of a particular amount of energy, thus reducing the body's energy state by that amount of energy down to a lower energy state. This amount of energy is also recognized as the amount of work performed by the body to produce that photon. The photon itself represent the work performed by the body.

*Black Body*model**2. Photon's Energy**

Once Max Planck realized the relationship between temperature, emission and wavelength, he reworked the algebra to solve for any given photon's energy, given its wavelength. This equals the amount of work performed by a black body to produce a given photon.

*Photon_Energy = Plancks_Constant * Frequency*

*Photon_Energy = Plancks_Constant * Speed_of_Light / Wavelength***3. Black Body Power for a Given Wavelength at a Given Temperature**

Once the amount of work is known for a given quatum emission, i.e. photon, of a given wavelength, the emission power over time of that body at a given temperature for a given wavelength is calculated as such:

**Radiance_Power (**Wavelength, Temperature**) =****{2 * Plancks_Constant * Speed_of_Light**^{2 }**/ Wavelength**^{5}**}*********{****1 / [e**^{(Plancks_Constant * Speed_of_Light / [Wavelength * Boltzmann_Constant * Temperature])}**-1]****}**