When an object is heated, its warmth can be felt from a distance. This is because the hot object tends to radiate the heat energy in the surroundings. The more be the temperature of the object, the more is energy radiated, and hence more warmth is felt by the person standing close to it. One of the prime misconceptions regarding energy radiations is that only a hot object is able to radiate heat energy; however, as per the physical laws of nature, if the temperature of an object is not at absolute zero (0K or -273°C or -459°F), it emits energy in the form of radiation. Stefan-Boltzmann law effectively establishes a relationship between the temperature of an object and the heat radiated by it. The rate at which the heat is radiated by an object, that is not present at absolute zero temperature, is proportional to the surface area of the object. This means that the more the surface area of the object the more will be the thermal radiation. Also, the radiations are proportional to the temperature of the object. More the temperature of the object more will be the energy density, and therefore, more will be the radiation rate. It has been experimentally found that the thermal radiations are proportional to the fourth power of absolute scale temperature. The combination of these two proportionalities gives us the Stephan-Boltzmann law for the perfect black body. For any substance, other than a perfect black body, the rate of transfer is comparatively lower because a black object is the best radiator of energy, and it radiates more heat than an ordinary object. In the case of the objects other than the black body, their emissivities are taken into consideration, the value of which lies between 0 and 1. Stefan-Boltzmann law is also known as Stephan’s fourth power law. It was experimentally derived by Slovenian physicist Josef Stephan in the year 1879 and was theoretically verified by Austrian physicist Ludwig Boltzmann in the year 1884. The constant of proportionality used here is known as the Stefan-Boltzmann constant, which is represented by the Greek letter “σ” (sigma) and has the value equal to (5.67 x 10-8W/m2K4).
Examples of Stefan-Boltzmann Law
1. Calculating Radius of Stars
To calculate the radius of a star, its luminosity is taken into consideration. The luminosity is the total power discharged by the star in space. It depends on two factors, i.e., the temperature and surface area. The relationship between the temperature of an object, the surface area of the body, and the rate of radiation discharge is given by the Stephan-Boltzmann law. Hence, it can be used to calculate the radius of a star.
2. Heating Iron Rod
When an iron rod is heated at one end, the heat tends to spread and reach the opposite end of the rod after some time. One of the common misinterpretations is that the energy transfer only takes place from the hot end of the rod to the cold end of the rod; however, the truth is that both the cold and hot ends of the rod exhibit thermal radiations in the environment. The difference is that the hot object radiates more than the colder one. Therefore, the net flow of heat is from the hot end to the cold end. This is one of the finest examples that effectively demonstrates Stephan-Boltzmann law in real life.
The sparklers make use of the Stephan-Boltzmann law to emit glittery chemical particles in the environment. When a firecracker or a sparkler is lit, it undergoes a significant increase in temperature. According to the Stephan-Boltzmann law, the temperature of the object is proportional to the energy radiated by it, which is why the sparkler appears less shiny in the beginning and gets lustrous afterwards.
4. LPG Gas Stove
Cooking food on a gas stove is the best example to observe Stephan-Boltzmann law in real life. The heat energy generated by the burner does not reach the utensil or the food directly but follow a radiative path. The rate of transfer of radiations is proportional to the size of the object, which is why smaller burners radiate energy at a slower rate as compared to large-size burners.
A bonfire is often used during winters to keep the surroundings warm. The warmth produced by the bonfire can be easily felt from afar. This effectively makes use of the Stephan-Boltzmann law because the heat energy is emitted in the surroundings in the form of radiations.
The welding process is used to join the two pieces of metals together by heating them and allowing the melted parts to fuse together. The fused parts are then subjected to immediate cooling. The spark produced during the process of welding can be easily seen around the welding torch from a distance. This is because the energy is being radiated in the surrounding. Hence, the application of Stephan-Boltzmann law can be easily seen.
7. Calculating the Emissivity of an Object
The emissivity of an object can be calculated by computing the ratio of the rate of radiation of the object in consideration and the rate of radiation of a perfect black body. The only condition is that the surface area and temperature of both objects must be the same. To maintain the same physical condition for both the objects, they are placed in the same environment, and the size of the objects is confined to the unit area. The rate of radiation of the perfect black body or any other object is given by the Stephan Boltzmann law. Hence, the calculation of emissivity is one of the prime applications of Stephan Boltzmann law.
8. Aluminium Foil
Stephan-Boltzmann law explains a lot about the emissivity of an object. It states that if an object has a low value of emissivity, the rate at which the radiations would escape from the object would be very less. The emissivity of an aluminium foil is very small, approximately equal to 0.1 units. This is the reason why food stored in aluminium foil stays warm for a longer duration.