00:01
Stars are often considered to be perfect black bodies.
00:06
And so we're going to see what we can find out about a nearby white dwarf star called sirius b is a type of star known as a white dwarf with a very high temperature, much hotter than the sun.
00:29
But we're going to see what else we can determine about this star.
00:34
So the black body radiation, we're going to write down a couple laws.
00:38
That govern black body radiation.
00:41
The first one is the stefan boltzmann law.
00:49
What this formula relates is the flux or intensity of radiation from a black body, which is defined to be the power radiated per unit surface area, is equal to, well, write it down for perfect black body, something called the stefan boltzman constant, times t to the fourth.
01:17
The steph bond -boltzman constant is often considered to be a fundamental constant, but it is related to things like the boltzmann constant and the plank constant.
01:34
So it kind of merges thermodynamics with the quantum theory, and its units are watts per meter squared kelvin to the 4.
01:48
Fourth power.
01:52
And as i mentioned, the intensity is the power radiated by the black body, divided by its surface area.
02:04
Okay, so for this star, if we know its temperature, we can determine its intensity.
02:11
It simply put in our temperature and our stefan boltzmann constant.
02:19
And we may not have much feel for the number that comes out, but it will be in watts per meter squared.
02:33
So the intensity of series b is 1 .88 times 10 to the 10th watts per meter squared.
02:47
And like i said, we don't have much feel for this.
02:50
So what we're going to do is we are told that the total power radiated by this star is about 10 to the 25th watts.
03:06
Okay, so that's the total power, not the power per unit area.
03:11
But by knowing this and knowing that the power per unit area is the intensity, we can determine the surface area of the star, and therefore we can determine its radius by assuming that it's a sphere, with an area of 4 pi times the radius squared.
03:38
That's the surface area of a sphere.
03:50
Okay, so i'm kind of just working through the algebra.
03:57
We have the power, and we have the intensity.
04:12
So again, this is not something we probably have much feel for.
04:19
Yeah, it's just a very large number.
04:35
Yeah, 1 -9.
04:39
I'm not 3 -1 -9.
04:41
Times 10 to the 14th meter squared.
04:47
Again, we don't have much feel for that, but let's figure out the radius of this star, and then we'll compare it to some known objects in our own solar system.
05:02
So radius is then the square root of the area over 4 pi.
05:21
And we can see that it's going to be about something of the order of 10 to the 6th meter.
05:30
Yes, indeed.
05:33
It is 6 .5 .1 times 10 to the 6 meters.
05:42
Okay, so to get a feel for this, let's take a look at our sun...