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**Thermal Radiation Short Notes**

**What is Radiation?**

- Radiation is the energy emitted by matter in the form of electromagnetic waves.
- Here we will look into thermal radiation (10
^{-7}m to 10^{-4 }m) since we are dealing with heat transfer. - In radiation, the internal energy of an object decreases.

**Rate of emission of radiation by a body depends on-**

- Surface temperature
- Surface Nature
- Wavelength or frequency of radiation

**Read More- Convection Heat Transfer Process**

__Important Definitions__

__Important Definitions__

**Total Emissive Power (E)**

- The total amount of radiation (all wavelength range) emitted by a body per unit area and time.
- A/C to Stefan-Boltzman, for a black body emissive power, is proportional to absolute temperature to the fourth power.

E_{b} = σAT^{4} W/m^{2 }

σ = Stefan-Boltzman Constant (5.67*10^{-8} W/m^{2}K^{4})

**Monochromatic Emissive Power (E**_{λ})

_{λ})

- Rate of energy radiated per unit area of the surface per unit wavelength.
- At any given temperature the amount of radiation emitted per unit wavelength varies at different wavelengths. So, Monochromatic Emissive Power (E
_{λ}) of the surface is used.

**Emissivity (ε)**

- The ability of the body surface to radiate heat.
- It is also defined as the ratio of emissive power of a body to the emissive power of a black body of equal temperature.
- Its value varies for different substances ranging from 0 (white body) to 1 (black body).
- Emissivity may vary with temperature and wavelength.

**Irradiation (G)**

- Total incident radiation on a surface from all directions per unit time per unit area of the surface.

**Radiosity (J)**

- It refers to all of the radiant energy leaving a surface per unit area of the surface.

J = ε + ρG

ρ = reflectivity

**Reflectivity (**ρ**)**

- Fraction of incident radiation reflected.
- For white body :- ρ = 1, α = 0, τ = 0

**Absorptivity (α)**

- Fraction of incident radiation absorbed.
- For Black Body α = 1, ρ = 1, τ = 0

**Transmittivity (τ)**

- τ = 0 for black, white and opaque body (α + ρ = 1).
- The fraction of incident radiation transmitted.

**Read Also- Modes of Heat Transfer, Convection**

**Different Laws in Thermal Radiation**

These are the important laws we should know in order to understand and solve the problems of the Thermal Radiation Chapter in Heat and Mass Transfer.

**Stefan-Boltzmann Law**

According to this law, the total emissive power of a black body is directly proportional to the fourth power of its absolute temperature.

E_{b} = σT^{4}

σ is Stefan-Boltzmann Constant (5.67 × 10^{-8} W/m²K^{4})

**Kirchhoff’s Law**

This law states that at any temperature the ratio of total emissive power (E) to the total absorptivity (α) is constant for all substances which are in thermal equilibrium with the surroundings.

E/ α = constant

OR

The emissivity (ε) of a body is equal to its absorptivity (α) when the body remains in thermal equilibrium with its surroundings.

ε = α

**Planck’s Law**

The total emissive power of a Gray body varies with the wavelength at a given temperature and varies with the temperature too.

So, it’s a function of wavelength and temperature, i.e. E = f(λ, T)

Now According to Max Planck, the spectral distribution of the radiation intensity of a black body is given by –

(E_{λ})_{b} = p/q

Where p = 2πc^{2}hλ^{-5}

q = exp(ch / λkT) – 1

(E_{λ})_{b }= monochromatic emissive power

**Wien’s Displacement Law**

It gives a relationship between the temperature of a black body and the wavelength at which the maximum value of monochromatic emissive power occurs.

The product of wavelength (λ) and temperature (T) is constant.

λ_{max}T = constant = 2898 or 2900 µmK (Unit)

λ_{max} unit is micrometer

*Combining Planck’s Law and Wien’s Displacement Law results in the condition for maximum monochromatic emissive power for a black body.*

(E_{λb})_{max} = 1.285 × 10^{-5} T^{5}W/m^{2} per meter length

**Lambert’s Cosine Law**

This law states that the total emissive power E_{θ} from a radiating plane surface in any direction is directly proportional to the cosine of the angle of emission.

E_{θ} = E_{n}cosθ

Where E_{n} = total emissive power in the normal direction (of the radiating surface).

- The law is true for diffuse radiation surfaces.
- The diffuse radiation surface means the radiation intensity is constant.

*Note- Symbols have usual meanings.*

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