 Hi guys, welcome back to another episode of astrophysics and cosmology. What are the learning objectives for today? We are going to understand what is meant by a black body radiator. Later on in this video, we will discuss two very important laws related to radiation. One is called Stephen Boltzmann Law and second is called Wien's Displacement Law. At the end of the video, we will solve some numerical questions related to these laws with the help of relevant equations. So, what is black body? Black body is basically an ideal object which can absorbs and emits electromagnetic radiation. It means it is a perfect absorber and at the same time it is a perfect emitter of electromagnetic radiation. Sun is the best example of black body. It is an ideal black body because it absorbs and emits electromagnetic radiation. Not only the sun, there are millions of stars which are also the examples of black body. Let's move to Stephen Boltzmann Law. According to Stephen, the luminosity of a black body is the product of the size of the black body and the fourth power of the temperature. Here is the simple presentation of Stephen Boltzmann Law. So, mathematically, the luminosity according to Stephen Boltzmann Law is the product of a Stephen constant times area of the black body times temperature. The unit of luminosity is what? And the area in meters square and temperature in Kelvin. The fixed value of the Stephen Boltzmann constant is here on the screen. Black body radiation curves have quite a complex shape. As the temperature of the black body increases, the peak wavelength decreases. We will discuss this in Wien's displacement law as well. The intensity, I mean the flux of all wavelengths, increases as the temperature of the black body increases. Finally, the total energy being radiated is the area under the curve increases rapidly as the temperature increases. The Wien's displacement law or Wien's law is very simple. It shows the relationship between the color of black body and the temperature of black body. According to Wien's, the product of peak wavelength donated by lambda max and temperature is always constant which is 2.898 into 10 raised to power 3. Here is the Wien's law graph which shows the relationship between the color and temperature. On Y axis there is a power density whereas on X axis we have taken wavelength. You can easily observe that color of black body is going to be changed with temperature. A visible spectrum which is about 518 nanometer wavelength is also present here. Let's move to the final part which is the calculation with the help of Wien's law and Stefan Boltzmann law. Here is an example question. A sun behaves in an approximate black body radiator with this much wavelength. We have to prove that the temperature of the sun is 6000 Kelvin. We can simply use the Wien's law which is the lambda max and temperature product which has always an equal value or constant value which is 2.898 into 10 raised to power minus 3. What we have done here, we just substitute the value of lambda max which is already given in the question. Just replace the constant value and with the help of division we got 5570 which is approximately equal to 6000 Kelvin. This is another example to find out the luminosity with the help of the flux which is already given here 1.37 kW per meter square. What we have done here, we have used the formula of f is equal to L flux is equal to luminosity divided by 4 pi d square. We just substitute the value so luminosity will be the product of flux with 4 with pi with d square. Already the distance from sun and earth is already given. Finally, we can find out the radius of the sun with the help of formula L is equal to 4 pi r square and you know the constant and T power 4. So, the simple we have to substitute the value we have taken R as a subject formula and we can calculate accordingly. As you know making this kind of video requires a lot of time and efforts so please subscribe my channel and take great care of yourself. Take care, goodbye.