Let's start by studying the radiation coming from the Sun.
So we want to study the solar radiation.
And to, to make sure that it's not, that
our study is not contaminated by the presence of atmosphere.
So I'm, I'm going to study this extraterrestrial solar radiation, or the
solar radiation in space before this, before this solar radiation hits
the atmosphere of the Earth.
So plotted in this chart is what is called the spectral irradiance.
And it has a unit of watt per meter squared per nano meter.
So what this plotting over here, it's plotting the
intensity of light, that is, watt per meter squared.
And it's plotting it as a function of wavelengths.
It has a unit of watt
per meter squared and then as a function
of wavelength, which is given plotted on x axis.
So what we see over here is is this this so incoming solar
radiation or this solar irradiance plotted as a function of a wavelength.
It resembles very closely to this grey curve, which is indicated
as a black body spectrum, or this radiation from the sun.
It resembles very closely to.
Oh, what you expect from a black body, which is at
the same temperature of the sun, which is approximately 5800 Kelvin.
So, why this violet, first 4 slightly defray from the ideal black body spectrum?
The reason is that
the sun, even though we approximate it as a black body to.
To the first order but that's not exactly a black body, in fact, the sun has a
temperature of approximately 20 or 20 million Kelvins at the center of
the sun, and this is what causes, this is what causes the nuclear fission reaction.
Which converts hydrogen into helium,
and then at the surface of the sun is, is, is hydrogen, or is this hydrogen atom.
And this heat which is generated, it travels by convection up to
the surface, and then some of it is absorbed again by this hydrogen.
And it's finally emitted out in the form of this electromagnetic
radiation from the surface of the sun, which is at the temperature
of approximately 5,800 Kelvin.
So it's very close to a blackbody radiation, but,
it's, you know, those deviations that we are seeing are
because of the, because of these, all these reactions and
non-idiality is going on on the surface of the sun.
But anyway to the first order, we can approximate that as a blackbody spectrum.
So first
question to ask is what is a black body?
Blackbody is a body which absorbs all incoming radiation.
So let's say we have this object And we, you know, we have this incoming radiation.
We'll have outgoing radiation out of this.
So black body is a body in which you have no outgoing radiation at there.
Simply absorbs all the radiation which is incidental.
So a key
is to a first start an approximation. The way we can describe or we
can approximate these black body is by assuming
this cavity which is opaque to, opaque to incoming radiation.
So if we have this cavity and we have this small opening on this small
hole in this cavity and then we make radiation incident on it so this radiation
will go inside.
But it won't be able to come out because this, this black body
then is opaque to radiations that will have a lot of this reflection inside.
But it would, there is small probably that it will come out.
So this is a practical way in which you could you could you could,
you know, theorize or Experimentally study the radiation from a blackbody.
And this is exactly how Mr. Max Planck,
so he studied this radiation from apparatus like this.
And he described the properties of this blackbody radiation.
So I want to spend some time describing
how this blackbody radiation looks likes, because it
has a, a large amount of implications on
the efficiencies that we can get from solar cells
and, you know, in solar energy conversion in large.
So the first correct description of this
black-body radiation is often credited to Max Plank,
who derived this around 1900, and, that's why
this this law is called, is Plank's Law.
And, when I say that this intensity of
this of this blackbody radiation as a function
of frequency of this light and as a function of temperature
is given by this formula where it's proportional to
the, to the cube of this frequency, and
it's it's also dependent on that frequency by this
exponential term. Which has this exponential term, which has
frequency as it has temperature, and it's given by this formula.
We can also rewrite this formula to give this, give this intensity as
a function of wavelength, and it's plotted as a function of wavelength over here.
And we can express this frame formula, as a function
of wavelength, where it's again given by This formula,
where it's inversely proportional to the wavelength, using this term.
And then it has a exponential term over here.
Which has essentially, essentially lambda term over here as well.
Lamda as well as temperature term over here.
So these, these relationships
are what is called as, Plank's Law.
And plotted here is this intensity of the function of wavelength.
We can also locate in terms of the function
of a frequency, which will essentially increase with decreasing wavelength.
Because this frequency, you can simply write that, you know,
velocity of light is equal to the wavelength times the frequency.
So if
wavelength increases the frequency will decrease or vice versa.
So when wavelength increases, you can also plot
this as a function of, frequency over here.
So, looking at this curve, there are some unique features that we see.
So we see that, We see that as you increase the temperature of the blackbody.
So the temperature is featuring in this equation over here.
So as you increase
the temperature of the body, blackbody.
What you are seeing is that the total intensity.
This total energy, which is represented by the total area under this curve.
So total intensity, total watt per meter squared.
This is watt per meter squared per nanometer.
If we'll integrate it, so this would be watt per meter square.
So this total intensity,
it essentially increases as you increase,
increase the temperature of your black body.
And this is kind of expected if, you know, if you have a, if you have a
hotter body you would expect that it will have
it will emit a larger aura intensity of light.
In fact we can the way we can express this is we
can integrate this intensity as a function of frequency for all frequencies from
zero to infinity.
And then the result that we get is
essentially this total power, or this total intensity.
It's proportional to, to, it's proportional
to the fourth power of the temperature.
And in fact, it's only a function of the temperature, and this is what is also
called as Stefan-Bosman law. And another thing that we see
in this spectrum is that as we increase the temperature the wave length, the
wave length at which this peak of
this intensity is occurring, it actually decreases.
So, as we are increasing the temperature, the wave length at
which this maximum is occuring This maximum is occurring is decreasing.
And this is, in fact, can also be expressed analytically and
often it's expressed this maximum wavelength is essentially
given by as a function of temperature just by
the simple relationship where this is Inversely proportionate
to the temperature of our of our black body.
And this is also known as Wein's Displacement Law.
And this can again be derived
by taking a derivative of this derivative of this equation
as a function of wavelength over here, and then equating
it to zero, and that would give you essentially a
maximum wavelength, which depends upon, which depends upon the temperature.
So these are, you know, some features of features of this blackbody radiation.