## Blackbody Radiation

It is known that the amount of radiation energy emitted from a surface at a given wavelength depends on the **material** of the body and the condition of its **surface** as well as the surface **temperature**. Therefore, various materials emit different amounts of radiant energy even whhen they are at the same temperature. A **body** that emits the **maximum amount** of heat for its absolute temperature is called a **blackbody**.

A **blackbody** is an idealized physical body, that has specific properties. By definition, a black body in thermal equilibrium has an **emissivity** of ** ε = 1.0**. Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a black body and therefore are called gray bodies.

The surface of a blackbody emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature (25 °C, 298.15 K). Real objects with emissivities less than 1.0 (e.g. copper wire) emit radiation at correspondingly lower rates (e.g. 448 x 0.03 = 13.4 W/m^{2}). **Emissivity** plays important role in heat transfer problems. For example, solar heat collectors incorporate selective surfaces that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation.

Since the **absorptivity** and the **emissivity** are interconnected by the **Kirchhoff’s Law of thermal radiation**, a **blackbody** is also a perfect absorber of electromagnetic radiation.

**Kirchhoff’s Law of thermal radiation**:

*For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.*

A **blackbody** absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. Its **absorptivity** is therefore equal to unity, which is also the highest possible value. That is, a **blackbody** is a **perfect absorber **(and a **perfect emitter**).

Note that visible radiation occupies a very narrow band of the spectrum from 0.4 to 0.76 nm, we cannot make any judgments about the blackness of a surface on the basis of visual observations. For example, consider white paper that reflects visible light and thus appear white. On the other hand it is essentially black for infrared radiation (**absorptivity α = 0.94**) since they strongly absorb long-wavelength radiation.

## Blackbody Emissive Power

The **blackbody emissive power**, **E _{b} [W/m^{2}]**, from a blackbody to its surroundings is proportional to the

**fourth power**of the absolute temperature and can be expressed by the following equation:

*E _{b} = σT^{4}*

where **σ** is a fundamental physical constant called the **Stefan–Boltzmann constant**, which is equal to** 5.6697×10**^{-8}** W/m**^{2}**K**** ^{4}** and T is the absolute temperature of the surface in K.

The term **blackbody** was introduced by a German physicist Gustav Kirchhoff in 1860. **Blackbody radiation** is also called **thermal radiation**, cavity radiation, complete radiation or temperature radiation. Three following laws are associated with blackbody radiation:

**Kirchhoff’s law.**This law gives the relationship between the emissivity and absorptivity of an object.**Planck’s law.**This law describes the spectrum of blackbody radiation, which depends only on the object’s temperature.**Wien’s displacement law.**This law determines the most likely frequency of the emitted radiation.**Stefan–Boltzmann law**. This law gives the radiant intensity.

All bodies above absolute zero temperature radiate some heat. The sun and earth both radiate heat toward each other. This seems to violate the Second Law of Thermodynamics, which states that **heat cannot spontaneously flow** from cold system to hot system without external work being performed on the system. The paradox is resolved by the fact that each body must be in direct line of sight of the other to receive radiation from it. Therefore, whenever the cool body is radiating heat to the hot body, the hot body must also be radiating heat to the cool body. Moreover, the hot body will radiate more energy than cold body. The case of different emissivities is solved by the **Kirchhoff’s Law of thermal radiation**, which states that object with low emissivity have also low absorptivity. As a result, **heat cannot spontaneously flow** from cold system to hot system and the second law is still satisfied.

## Spectrum – Blackbody Radiation

The Stefan–Boltzmann law determines the total blackbody emissive power, E_{b}, which is the sum of the radiation emitted over all wavelengths. Planck’s law describes the **spectrum of blackbody radiation**, which depends only on the object’s temperature and relates the spectral blackbody emissive power, E_{bλ}. This law is named after a German theoretical physicist Max Planck, who proposed it in 1900. **Planck’s law** is a pioneering result of modern physics and quantum theory. **Planck’s hypothesis** that energy is radiated and absorbed in **discrete “quanta”** (or energy packets) precisely matched the observed patterns of blackbody radiation and resolved the **ultraviolet catastrophe**.

Using this hypothesis, Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by:

is the spectral radiance (the power per unit solid angle and per unit of area normal to the propagation) density of frequency*B*_{ν}(v,T)*ν*radiation per unit frequency at thermal equilibrium at temperature T**h**is the Planck constant**c**is the speed of light in a vacuum**k**is the Boltzmann constant_{B}is the frequency of the electromagnetic radiation*ν***T**is the absolute temperature of the body

The **Planck’s law** has the following important features:

- The emitted radiation varies continuously with wavelength.
- At any wavelength the magnitude of the emitted radiation increases with increasing temperature.
- The spectral region in which the radiation is concentrated depends on temperature, with comparatively more radiation appearing at shorter wavelengths as the temperature increases (
**Wien’s Displacement Law**).