Planck’s Radiation Law Video Lecture - Civil Engineering (CE)

[Music]
hello everyone and welcome to Skye
scholar the channel where you can learn
about new concepts in physics and
astronomy I am your host dr. Robitaille
I am eager to talk to you about the
solar spectrum but first we have to
cover black bodies and the law is
advanced by Wien Stefan and Planck then
we will tackle kirchoff's law and
finally get to the spectrum of the Sun
in our previous video we covered
radiative heat transfer and Stuart's law
we also learned that the emissive
properties of objects do not typically
change with temperature in an easily
predictable manner
but there is one class of objects where
the emissive properties are closely
related to temperature these are called
black bodies and they are the subject of
today's presentation let's start at the
beginning of the 1800s even the late
1700s and follow the line of reasoning
outlined in my paper on blackbody
radiation and the carbon particle which
is linked below in the 1800s mankind had
discovered that objects which are made
of graphite are covered with soot or
lampblack produced a very unusual type
of light these objects were different
than any other objects and they became
known as black bodies as a result the
type of light that was produced was
called blackbody radiation or normal
radiation but it would have been better
called special radiation because it was
nothing normal about it the light or
radiation produced by black bodies was
unusual because it was continuous but
more importantly scientists could infer
the temperature of the emitter by
analyzing this light blackbody radiation
was linked in an easily described and
smoothly changing manner to temperature
no other radiative process in nature had
this property you can see the
relationship of blackbody radiation with
temperature in this figure the
horizontal axis represents wavelength of
the light emitted in nanometers which is
one billionth of a
Peter the vertical axis represents
intensity as the temperature of a black
body is increased the emitted light
changes in a predictable manner the
position of the maximal ignition moves
to shorter wavelengths this observation
was formulated into a law by William
Wien in 1896 which is known as wings
displacement law it states that the
product of the maximum wavelength for
the emission times the temperature
always equals a constant be known as
Wiens displacement constant the equation
can also be expressed in terms of
frequency with appropriate changes in
winds constant in 1879 Joseph Stefan
discovered something else about
blackbody radiation the area under the
curve is equal to another constant Sigma
times the temperature to the fourth
power this became known as Stefan's law
and Sigma is known as the Stefan
Boltzmann's constant but it was not
until Max Planck came along in 1901 that
the full equation for blackbody
radiation was formulated Planck's
equation described the shape of the
blackbody curve in terms of only two
variables wavelength and temperature
alternatively Planck's equation like
wings could also be expressed in terms
of frequency this is the central
equation in dealing with blackbody
radiation and that is why it is so
important with the discovery of the
equation for blackbody radiation
Planck became known as the father of
modern physics that is because Planck's
law introduced the concept of the
quantum and the field of quantum
mechanics was born you can see the
introduction of a quantum in the H nu
terms H is known as Planck's constant H
times nu became known as the quantum of
action and represents the energy
associated with the photon at different
frequencies
in addition Planck's equation contains
another constant denoted by a lower
letter K this is known as Boltzmann's
constant and it has a precise value it
is related to the conversion of kinetic
energy at the microscopic level to
temperature at the macroscopic level we
will learn more about this
dealing with the second law of
thermodynamics and the concept of order
in an idealized system for now all you
have to remember is that Planck's
equation relates the intensity of
radiation produced at a given
temperature to either frequency or
wavelength interestingly you can derive
both Wiens law and stephon's law from
Planck's equation using calculus the
first derivative of Planck's equation
produces Rives law while the integration
results in Stephan's law of course
everyone can no Wiens law and stephon's
law without ever learning calculus you
are now beginning to see why blackbody
radiation
excited the scientific community not
only did it give rise to the idea that
physics was quantized but if you lived
in the middle of the 1800s
you could also know the temperature of
an object simply by analyzing blackbody
radiation but how is this done in
practice scientists had already gotten
into the habit of building cavities in
order to study blackbody radiation these
were usually built from graphite the
same material found in a pencil if the
walls of the cavity were not made from
graphite they were typically covered
with soot or lampblack which was black
carbon from the inside of oil lamps this
was one of the best absorbers the walls
of the cavity could not be transparent
they had to be opaque a small hole was
drilled into one wall to allow
scientists to sample the light inside to
measure the temperature of an object
scientists inserted a few extra dividers
in the cavity and plays a sample near a
distant wall beyond the direct view of
the small hole after waiting for the
temperature to reach equilibrium the
radiation inside the cavity could become
black or normal and the temperature of
the object could be determined from the
blackbody spectrum the process could be
repeated many times to ensure that the
cavity temperature was adequately rate
is prior to the final reading for
example the temperature of an object
coming out of a hot oven could be
determined with great accuracy by
placing it inside a black body cavity
which was at thermal equilibrium with it
in this regard it is important to
remember
black bodies tend to be heated cavities
for example this can be achieved by
placing them in a heated oil bath or by
devising some electrical means to raise
their temperature in closing remember
the lessons learned so far different
objects typically emit radiation which
has an uncertain relationship with
temperature but this is not the case for
black bodies these objects are special
because they have a strong relationship
between their temperature and the light
that they emit we also learned that this
relationship can be described by the
laws of wing Stefan and Planck in our
next video you will learn about
kirchoff's law if you want to understand
modern astronomy and its pitfalls there
is no more important relationship to
learn in the meantime I hope that you
enjoyed this video on blackbody
radiation and some of the laws of
emission if you did please leave a like
in addition subscribe to join me as we
look more closely at the Sun the stars
and beyond comments are always welcome
down below I'll see you soon on our next
video
[Music]