00:01
Now given in this question is the planx radiation law and we want to use it to find or to derive the steffens -boltzmann's law.
00:14
Now the planx radiation law describes the intensity of radiation for a particular wavelength and a particular temperature.
00:26
On the other hand, the steffens -boltzman law tells us what is the total part of the power that is emitted by the black body, basically the total intensity emitted by the entire black body for any given temperature tea.
00:53
Now what this means is that it encompasses all the different wavelengths of radiation into the or the intensity.
01:08
It's like the total intensity of all the wavelengths whereas for the planx law is the intensity for individual wavelengths.
01:23
So therefore in order to find this what we have to do is to integrate this with respect to lambda throughout all the lambda.
01:35
So integrate i respect from lambda zero to lambda equals to infinity.
02:05
Of course the question wants us to simplify this a bit by doing some substitution, to substitute in x which is defined as hc over lambda kt.
02:30
Now we know that we also have to change the limits as well.
02:35
So when lambda goes to 0 ,000, 0, our x goes to infinity, and also when lambda goes to infinity, x goes to 0.
02:50
So the limits will swap, and also the integral, the lambda, we have to change it to the x, which is from here this equation, the x must be equals to negative 1 over lambda square, it's c over k t times, the lambda.
03:16
So d lambda equals to negative lambda square k t over hc times d x.
03:30
Of course we want to replace all the lambda into x so since we have a lambda square over here this must be equals to 1 over x square but of course x square in involves k t, right, you have a kt square and also a hitch c square...