# Thermal radiation and concept of a black body

Thermal radiation as a mode of heat transfer is electromagnetic mechanism that allows heat to be transfer to be transferred across a system boundary or void matter with the speed of light which is solely caused by a difference in temperature and not the nature of material. This mode of heat transfer does not require a medium unlike other mode of heat transfer. Thermal radiation explains the consequence of radiant energy emitted from a body. This phenomenon is always explained by the activities of heat transfer in a thermos flask, incident rays of solar explosion, combustion chambers, space application and electron bombardment are examples of thermal radiation.

When a radiating body releases a non continuous but successive packet of energy called photons on another body which is caused by the molecular interaction in the radiating body, this brings about the rise and fall of energy level of the radiating body and these photons are propagated into space as rays. These are considered as electromagnetic waves with different frequency levels but with speed of light and travels in a straight line, on reaching the receiving body exerts three things: the body absorbs the rays, reflects the rays or transmits the rays. This is also illustrated when two bodies of different temperature levels placed together in an enclosure, the temperature from the hotter body is emitted and it is received by the cooler body by absorption, this transfer is the heat energy transfer by radiation. This makes the energy of the hotter body to decrease, this process continues until  an equilibrium is reached between the emitting body and the absorbing body and the radiation heat of absorption and  the temperature attainment to equilibrium is known as radiation energy.

The propagation velocity of radiation is equal to the speed of light and given by the relation: C = λf  …………….(1)

The energy of the photons is given by E = hf………..(2)

From equation (1) and (2),  E=  h*c/λ

Where h= plank’s constant= 6.624 *10-34 js

λ = the wavelength of the emitted ray

c= speed of light = 3*108 m/s

The factors affecting emission rate include: temperature of surface, nature of the surface and wavelength of the radiation.

these formulas are useful in classical physics and mechanics.

Absorptivity (α) is the ratio of the absorbed ray to total incident energy.

Reflectivity (ρ) is the ratio of the reflected ray to incident ray

Transmittivity ( τ) is the ratio of transmitted ray to incident ray.

Therefore       α +ρ +τ  =  1

Notice that all solid Engineering materials are opaque to thermal radiation and therefore   (ρ =0).

Also under industrial application monatomic and diatomic gases such as oxygen and argon which are radiate weakly even at high temperature neither absorb or emitted an appreciable amount of radiation energy while poly-atomic gases like sulphur(iv)oxide, ammonia and carbon(iv)oxide absorb and emits appreciable radiation energy.

When the angle of incident ray is equal to angle of reflection, specular reflection phenomena occurred, when incident radiation is distributed uniformly in all direction on a surface, it is called diffuse phenomena.

A gray body is one whose absortivity is constant over the entire frequency range and it’s absortivity does not vary with temperature and wavelength of incident ray.

A white body totally reflects all incident rays.

# Concept of black body

A black body is a hypothetical material that absorbs all radiant energy reaching it’s surface. There is no actual black body in existence, although certain materials do approach blackness. It is assumed that a black body absorbs all radiant energy with any small space that allows the rays to penetrate and diffuse inside the body like the movement of action in a closed vessel.

The proportionality between an e- missive of a black body and absolute temperature is given by Eb =αT4

Whereα =is the steffan Boltzmann constant (5.67*10-8W/m2T4)

Steffan Boltzmann law states that the total emissive power of a body is proportional to the forth power of the absolute temperature. This is a consequence of thermodynamics and electromagnetism principles.

The distributive of energy in a spectrum of a black is detailed accurately by plank’s law:

${W}_{B}=\frac{2\pi {c}^{2}{\lambda }^{–5}}{Exp\left(\frac{hc}{KT\lambda }\right)}$

Where;     Wb = monochromatic emissive power of black body

h = plank constant

c =speed of light

λ= wavelength of radiation

K = Boltzmann’s constant (1.3805*10-23 j/K)

T= absolute temperature.

Also by Kirchhoff’s law which states that the ratio of the total emissive power (E) is a constant for all substances which are in thermal equilibrium with it’s environment.

A1E1 = α1A1Eb   and in varying condition,

A2E2 = α2A2Eb

Also by wien’s law of displacement which states that the product of λMAXT = constant = 2898µmk and the law holds for some real substance but vary with absolute temperature in some metallic conductors.

you may wonder why a chemical Engineer needs this? it is because in the industry heat ex-changers you deal with and the reactors you design all deals with heat and in one way or another you must use any of the modes of heat transfer

References: Unit operation of chemical Engineering by Mccabe Smith Harriott

Heat and mass transfer by Er. R.K Rajput