Different Laws in Thermal Radiation

These are the important laws we should know in order to understand and solve the problems of 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.

Eb = σT4

σ is Stefan-Boltzmann Constant (5.67 × 10-8 W/m²K4)

  • 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


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 –

(Eλ)b = p/q

Where p = 2πc2-5

q = exp(ch / λkT) – 1

(Eλ)b = monochromatic emissive power

  • Wien’s Displacement Law

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

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

λmaxT = constant = 2898 or 2900 µmK (Unit)

λmax unit is micro meter

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

(Eλb)max = 1.285 × 10-5 T5W/m2 per meter length

  • Lambert’s Cosine Law

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

Eθ = Encosθ

Where, En = total emissive power in the normal direction (of the radiating surface).

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

Note- Symbols have usual meanings.