Wein’s Distribution Law Video Lecture - Civil Engineering (CE)

blackbody radiation and vinz law you'll
be aware that a red object appears red
because it reflects red light and
absorbs all other colors of the spectrum
equally a black object absorbs all
colors it will also when heated emit all
colors to form a continuous spectrum
this is what is known as blackbody
radiation this shape represents a
horseshoe being heated by a blacksmith
as it gets hotter it will emit more
radiation but also the proportion
emitted at different wavelengths will
vary and we'll see this in the color
change initially it will go dull red
then bright red through to orange
eventually becoming yellow and if heated
sufficiently will become white-hot and
then even take on a bluey tinge
we say the same colors with stars at
different temperatures cooler stars can
appear red the Sun is clearly yellow and
hotter stars can take on a bluey tinge
let's look at this in a little bit more
detail here we have a graph of the
intensity of the radiation against
wavelength for a black body which could
be a star I've put on the visible part
of the spectrum just for reference this
is a star at around 3000 Kelvin you'll
see it gives off a small amount of
radiation at the high-energy short
wavelength radiation it's peaking beyond
the red part of the spectrum and then
falls off towards even longer
wavelengths if we look at a different
star at say 6000 Kelvin we'll see that
overall this is a higher curve the
hotter star is giving off more radiation
but it's also peaking further to the
left so it's giving out for great
proportion of its radiation at higher
energy shorter wavelengths this star
would be giving off a significant amount
of light in the visible part of the
spectrum and our son is at roundabout
6000 Kelvin at 12,000 Kelvin this star
has a higher line still it's giving off
more radiation but now the bulk of the
radiation is at shorter wavelengths than
visible light this star would have a
bluey tinge to it now for a clearer
comparison I'll plot the lines of
intensity against wavelength for black
bodies at several different temperatures
on the same axis starting off with a
line for an object at 3000 Kelvin the
4000 Kelvin object has a overall higher
line it gives out more radiation but it
also peaks at a shorter wavelength the
trend continues with 5000 Kelvin peaking
at a shorter wavelength still and
finally the 6000 Kelvin line which Peaks
here adding the visible part of the
electromagnetic spectrum just for
clarity you'll see this equates to
roughly the temperature of our Sun which
appears yellow
the peaks of the lines here here here
and here I'm going to refer to as lambda
max the wavelength lambda which we get
the maximum intensity of electromagnetic
radiation given off by the object if we
join these Peaks with this dotted line
we see there's a clear trend going to
shorter wavelengths as the temperature
of the blackbody increases this
relationship leads to Vin's law which is
that lambda max times the temperature in
Kelvin is equal to a constant point zero
zero to nine meters Kelvin
don't forget lambda max is the
wavelength at which the object gives off
its maximum intensity of radiation so if
we observe a star and find that its peak
wavelength is 0.75 micrometers we can
rearrange the equation above and put in
the values for the constant point zero
zero to nine and the lambda T max down
here and we get that the temperature of
the star is 3900 Kelvin