Stefan’s Law Of Radiation

Heat or energy is a part of the electromagnetic spectrum. It can be transferred from one point or body to another only by three methods – convection, conduction, or radiation. The transfer of heat can take place with or without a medium. Convection and conduction need a medium to transfer heat, whereas radiation needs no medium. When radiation falls on a body, it is either partially reflected back or absorbed by the body or transmitted through the body. When the radiation is totally absorbed by a body, it is called a black body. The black body radiation gives rise to Stefan’s Law of Radiation. In 1879, Joseph Stefan studied black body radiation, which was further investigated by Ludwig Boltzmann. The investigation is known as Stefan-Boltzmann law or Stefan’s law of radiation.

Statement of Stefan’s Law of Radiation

According to Stefan’s law of radiation, the total amount of energy radiated or emitted per unit surface area at an absolute temperature per unit time of an ideal black body is directly proportional to the fourth power of the temperature.

Radiate energy = Emissivity × Stefan’s constant × Area × (Temperature)4 

Mathematically,

E=eσAT 4

Where,

E: Radiate energy

σ: Stefans’s-Boltzmann constant

T: Absolute temperature in Kelvin

e: Emissivity of the material

A: Surface area of the body

The dimension of the radiate energy E is energy flux. Joules per second per square metre, or watts per square metre, is the SI unit of the radiated energy.

Stefan’s Constant

The proportionality constant used in the above equation of Stefan’s law is called Stefan’s constant. It is denoted by the symbol σ. The value of Stefan’s constant σ is 5.670367×10-8 Wm2K-4.

The SI unit is Wm2K-4. Here, m stands for metre, W stands for Watt, and K for Kelvin. The dimension of Stefan’s constant is [M1 T-3 K-4]. Stefan’s constant is used mainly for two things – for estimating the amount of heat a black body radiates and for the conversion of units. 

Examples Of Stefan-Boltzmann Law

• Welding

Welding is a process that joins the two pieces of metals together. It is done by heating them and allowing them to fuse together. During the process of welding, sparks can be easily seen. This is because the energy is being radiated into the surrounding. 

• Calculating the radius of stars

The radius of a star is calculated by its luminosity. The luminosity is the total power radiated by the star in space. It mainly depends on two factors, the surface area and the temperature. The relationship between the surface area of the body, the temperature of an object, and the rate of radiation discharge is given by the Stefan-Boltzmann law. 

• Aluminium Foil

Aluminium Foil is a great example of Stefan-Boltzmann law. The law explains much about the emissivity of an object. It states that the lower the emissivity of an object, the chances of radiation escaping the object are also very less. The emissivity of an aluminium foil is approximately 0.1 units, which is why the food stored in aluminium foils stays warmer for more time.

Problem Sums

1. Find the total heat radiated by the body inside a spherical black body at temperature T, given that the area of the body is A and emissivity 0.6.

According to Stefan’s law of radiation, energy radiated by the body of emissivity 0.6 is:

E=eσAT 4

Or E=0.6σAT 4

2.If a radius of a star is 1000 times that of the Sun and its luminosity is 10000 times of the Sun’s luminosity, find the temperature of the star compared to the Sun.

Ratio of Stefan-Boltzmann Law of the star to that of the Sun: