Sections
Temperature is illustrated by the thermometers with Celsius temperature scale and the obsolete Fahrenheit temperature scale in the adjacent figure below (local link / general link: thermometer.html).
The
thermodynamic variables
include
amount of heat energy,
temperature,
pressure,
volume,
density,
entropy,
matter phase,
and,
in general, chemical abundances.
How heat energy determines the MICROSCOPIC state of a system is also part of statistical mechanics (the microscopic version of thermodynamics or the microscopic complement to classical thermodynamics)---but we will largely skirt that.
We will NOT go into detail on thermodynamics, but we need to discuss briefly certain salient points.
Salient Points of Thermodynamics:
Thermodynamic equilibrium is the
state when the thermodynamic variables are
unchanging in time.
Thermodynamic equilibrium
is a timeless and lifeless state at the macro-level.
A body in thermodynamic equilibrium
does NOT change color, size, phase,
or chemical composition. It just stays as it is.
Microscopically, change continues to happen.
In gases
and
fluids, they can translate
and rotate and have internal motions.
In solids,
they can't translate or rotate usually, but they can
oscillate and have internal motions.
All kinds of microscopic processes can happen too:
e.g., chemical reactions
and transition.
But the reverse processes have to balance the forward processes.
There is detailed balance
in physics jargon.
Thermodynamic equilibrium is
easy to analyze and systems in thermodynamic equilibrium
are common, and so thermodynamic equilibrium
is very important.
Absolutely vital is that many systems evolve slowly enough in time that
they are in
thermodynamic equilibrium
to some approximation at every instant.
Such an evolution is
a quasistatic process.
Quasistatic processes
are common and allow us to stretch the
concept of thermodynamic equilibrium
to large realms of reality.
Quasistatic processes
are also useful in theoretical developments and understanding.
Of course, there are many systems NOT in
thermodynamic equilibrium
and NOT quasistatic.
Any system with
internal variations in
temperature
and/or energy flows is
NOT in
thermodynamic equilibrium
and NOT quasistatic.
Analyzing such complex systems is hard,
but, of course, it is done, often by breaking a
system
into component
subsystems
that are in
thermodynamic equilibrium
or are quasistatic.
For example,
the
Sun-space-biosphere
(SSB) system
which is explicated in the figure below
(local link /
general link: disequilibrium_life.html).
A naive first thought is that macroscopic scale
motions as outside
of thermodynamics,
but actually they must be considered inside thermodynamics.
Macroscopic motions affect the
thermodynamic variables
cited above and are affected by them: e.g., a macroscopic squeezing of
a sample can increase its pressure and
pressure can cause macroscopic motion
(e.g., in heat engines
and hydraulics).
What is heat energy?
Heat energy (or just
heat or
properly internal energy) is statistically
distributed microscopic energy of various forms.
Formal heat is transferred
heat energy.
But everyone I know when talking
says heat to mean
heat energy
and heat energy flow
(or the like) to mean the formal heat.
I think we should just give up formal heat since word
definitions should
follow common usage---but the dead hand of the past prevails on this issue---even for
the supreme authority Wikipedia.
Microscopic bonding energies of all kinds
(e.g., ionization energies,
chemical bond energies,
and nuclear bond energies)
and microscopic interation energies are all
field energies.
Note that thermal radiation
is often loosely used as a
synonym for
blackbody radiation---which is
OK as long as you know what you mean.
In thermodynamics, there
are two categories of quantities
(i.e., thermodynamic variables):
extensive quantities
and
intensive quantities.
An extensive quantity
is proportional to the mass or volume
or count of entities or some other measure of the size of a system.
Mass and volume
are themselves extensive quantities.
Heat energy
is another extensive quantity:
one just adds up bits of heat to get the total amount in a sample.
Intensive quantities
do NOT depend on the size of a system in any sense
(i.e., they are independent of the scale of the system)
and are often ratios.
For example, density (which is the ratio of
mass/volume)
is an
intensive quantity.
A system of any size can have any density.
Temperature
(which we discuss in
subsection Temperature in Thermodynamics
just below) is another
intensive quantity, but
it is NOT a ratio in obvious sense.
For some explication of
scaling laws (AKA power laws),
see the figure below
(local link /
general link: scaling_law_size.html).
Temperature is actually
a darned hard thing to define completely in its most fundamental modern sense without knowing
statistical mechanics.
A stab at an incomplete modern fundamental definition is as follows:
It is essentially a sort of microscopic average energy, but by ancient convention
does NOT have the units
of energy.
Temperature was used in less
fundamental ways before the modern fundamental definition was established.
Originally, temperature may
have been NO better defined that what one reads off a
thermometer---but yours truly
does NOT know the evolution of the meaning of the term
temperature.
For example, if a system is all at one
temperature, it is all
in thermodynamic equilibrium
with itself---in the
temperature
thermodynamic variable sense
though NOT necessarily in all
thermodynamic variables
(e.g., pressure).
The unit of the Kelvin temperature scale
is the kelvin degree (equal in size to the Celsius degree).
There are no spontaneous heat flows at the macroscopic level
between objects of the
same temperature: they are in thermodynamic equilibrium with
respect to each other.
Note quantum mechanics
dictates that there is an irremovable amount of energy,
the zero-point energy.
So there is a coldest:
absolute zero.
However, there are
negative temperatures
on the Kelvin scale.
This remarkable fact is explicated in the figure below
(local link /
general link: 1919_solar_eclipse_negative_thermo.html).
Thermodynamics has always
been an eminently practical science.
It is the science
needed for heat engines
and
refrigerators.
For a schematic diagram of
a heat engine,
see the figure below
(local link /
general link: heat_engine_schematic.html).
Atoms
and
molecules move around.
Temperature, among other things, is a measure of
thermodynamic equilibrium.
An unchanging system all at one temperature is
in overall thermodynamic equilibrium.
In formal discourse as in
textbooks,
heat
(meaning heat energy)
and formal heat
are different things.
A short list of heat energy forms follows:
Temperature is
parameter
that controls the distribution of particles among microscopic states:
which are usually called
energy levels.
The figure below
(local link /
general link: maxwell_boltzmann_distribution.html)
explicates how temperature
controls the distribution of particles
among energy levels
in the special case of the
Maxwell-Boltzmann distribution
for an ideal gas.
Recall from IAL 1: Scientific Notation, Units, Math, Angles, Motion, Orbits that
in this course we usually only use the
thermodynamic temperature scale
or, as it is often called, the
Kelvin temperature scale.
Recall
T_K=T_C+273.15
and Absolute zero is T_K = 0 kelvin or T_C = -273.15 C.
Question: We put a cup of hot coffee and a vat of
hot water in thermal contact (i.e., we allow
heat transfer processes to
operate) and isolate them from the rest of the world
and NOTHING happens to either.
Absolute zero is the state
where all microscopic kinetic energy that can be removed from a system has been removed.
Answer 3 is right.
The figure below
(local link /
general link: internal_combustion_engine.html)
illustrates how the schematic
heat engine
is realized by the
internal combustion engine (ICE).
Some examples of
blackbody radiators,
approximate ones,
and variations from them are discussed below:
The filament of an incandescent light bulb. See the incandescent light bulb filament in the figure below (local link / general link: light_incandescent_filament.html).
Flames
under ordinary laboratory conditions
have temperatures
∼ 2000 K
(see Wikipedia: Flame: Color).
However,
under ordinary laboratory conditions they are too dilute to
radiate like blackbody radiators.
Their spectrum is
a mixture of an
emission line spectrum
and some degree of
blackbody radiation.
The flame color
depends on temperature,
the type of fuel,
the premixing of molecular oxygen (O_2),
and other things probably.
The upshot is that flame color
is NOT necessarily the
color
the human eye sees for
blackbody radiation
at flame
temperatures.
A stove grill that is red-hot. It's actual temperature
must be much lower than 1000 K---just guessing.
If the guess is right, its blackbody-spectrum peak is at
∼ 3 μm
(from Wien's law:
see below section Wien's Law)
which is in the
IR (infrared).
The human body
(illustrated abundantly in the figure below
(local link /
general link: beach_bondi.html)
has fiducial temperature 310 K
(see Wikipedia: Human body temperature)
and, therefore has its
blackbody-spectrum peak at
∼ 10 μm
(from Wien's law: see below)
which is well into
IR (infrared).
Stars, including
the Sun,
approximate blackbody radiators
which is a key reason for studying
blackbody radiators here.
A useful experimental setup that is a near-perfect
blackbody radiator
is a completely closed oven---which in ancient physics
jargon is called a hohlraum.
The walls of the oven are held to uniform temperature
and emit pure
blackbody radiation
at that uniform temperature.
The walls also absorb and reflect that
blackbody radiation,
but all processes cancel out and a
detailed balance
is maintained with
electromagnetic radiation (EMR)
inside the hohlraum
in thermodynamic equilibrium
with the walls.
The EMR
inside the hohlraum is near perfect
blackbody radiation.
A small, negligibly perturbing aperture
allows one to study the radiation field.
The blackbody spectrum
obtained is more perfectly blackbody-like than almost an in
nature.
The
cosmic microwave background (CMB)
(which we discuss in section
Wien's Law below)
is one of nature's most
near-perfect blackbody emitters.
Actually, any small aperture to an internally unilluminated closed space at human-scale temperatures
is a pretty good
blackbody in the sense of
NOT reflecting much though usually NOT in being
blackbody radiator radiating
a blackbody spectrum.
A useful toy that illustrates this is
the
Purcell's
blackbody box
or Purcell's
hohlraum: see the figure below
(local link /
general link: purcell_hohlraum.html).
Purcell's
hohlraum
is just box with a small hole for viewing the interior.
Very little visible light
can be reflected out of the viewing hole if small enough.
No matter what the interior color of
a Purcell's
holhraum, the hole looks very, very black.
The hole is a very perfect
non-reflecter: i.e., a blackbody.
A blackbody spectrum with
room temperature is being emitted from the hole, but that spectrum peaks well into the
infrared, and so we
CANNOT see it.
Nowadays, we can make very black materials which
are also close to being
blackbodies as REFLECTERS, but
NOT usually as emitters.
As an illustration of a very
black material,
see vantablack
in the figure below
(local link /
general link: vantablack.html).
Dense bodies with varying temperature are NOT
blackbody radiators,
but have spectra that are
mixtures of the blackbody spectra
at different temperatures.
Mixtures
of blackbody radiation
are in the general category of
thermal radiation---here
NOT used as a synonym
for blackbody radiation.
But we often just call mixtures of
blackbody radiation,
just mixtures of blackbody radiation
so that it is clear we are NOT using
thermal radiation
as a synonym
for blackbody radiation.
Of course, there are radiators that are NOT at all like
blackbody radiators:
e.g., dilute gases as we will discuss below.
As a recapitulation of this section, see
Blackbody radiation videos
below
(local link /
general link: blackbody_videos.html).
Wien's law (AKA Wien's displacement law) determines intensity maximum (in units of energy/(area*steradian*time*wavelength)) of a blackbody spectrum.
Wien's law is explicated in the figure below below (local link / general link: wien_law.html).
Examples of the use of Wien's law
are given in the table below.
From
Wien's law
you can determine the wavelength of maximum of EMR emission
for any body at a given temperature---insofar as that body approximates
a blackbody.
Wien's law
can be inverted, and thus if you know the shape of spectrum
that approximates a blackbody, you can estimate the temperature of
the emitting surface.
This is a crude, but very useful, way of finding star surface temperatures.
Recall Wien's law:
What approximately is the temperature of the background EMR field?
A very exact determination gives
CMB temperature T = 2.72548(57) K (Fixsen 2009)
As a preview for cosmology
(which we cover in
IAL 30: Cosmology),
we here consider the
cosmic microwave background (CMB, T = 2.72548(57) K (Fixsen 2009))
which turned up in question just above
in subsection
Examples of the Use of Wien's law.
The CMB
is a homogeneous and isotropic
background EMR
that permeates all observable universe.
It is a relic of the
recombination era
of the universe
which happened about 400,000 years after the
Big Bang.
According to the
Λ-CDM model,
the recombination era
is at 377,770(3200) years after the
Big Bang
(see decoupling era
at Wikipedia:
Λ-CDM model parameters).
The discovery in 1965 of the
CMB
was the crucial evidence that convinced most people that something like a
Big Bang
had happened.
The discovery is discussed in
IAL 30: Cosmology: The Cosmic Microwave Background (CMB).
_____________________________________________________________________________________
Table: Examples of the Use of Wien's Law
_____________________________________________________________________________________
Object Approx. T (K) Approx. λ_Max Comment
(microns)
_____________________________________________________________________________________
hot star 40000 0.075 far in UV
photosphere
Solar photosphere 5778 0.5015 the peak is
near the blue end of green light,
but the mixture of wavelengths
is dominated by yellow or white.
human body 310 10 in IR
-so we-all
thermally radiate
mainly
in the IR, but
reflect mainly
in the visible.
Pluto's surface 37 80 far in IR for blackbody radiation,
of course, we see Pluto by
reflected sunlight in the
visible. The images of Pluto
by the New Horizons spacecraft
are of relected light.
See New Horizons Pluto images.
_____________________________________________________________________________________
Question: The background EMR field that permeates all
space has a blackbody spectrum
and a peak at about 0.1 cm = 1000 microns
in the microwave band of the
electromagnetic spectrum
(Se-387).
λ_max ≅ 3000 μm·K / T .
Answer 3 is right.
T ≅ 3000 μm·K / 1000 μ = 3 K .
Speaking loosely, one could say the
CMB
is a relic of the Big Bang.
The CMB, in fact,
is a nearly perfect blackbody spectrum---one
of the most perfect in nature.
Experimental hohlraums can also be very perfect
blackbody radiators,
but are in experiment,
NOT nature.
See the CMB
in the figure below
(local link /
general link: cmb.html).
This law gives the total power per unit area (i.e., radiant flux (AKA flux)) emitted by a blackbody radiator.
This is the power per unit area summed/integrated over all wavelength.
For us, the importance of the Stefan-Boltzmann law is that it shows that the power of a radiator increases strongly with increasing temperature.
The Stefan-Boltzmann law is described in the figure below (local link / general link: stefan_boltzmann_law_logarithmic.html).
The blackbody
flux
emitted increases by a factor of:
If T_1 is the initial temperature and T_2=2T_1 is the raised temperature,
then
Form groups of 2 or 3---NOT more---and tackle
Homework 7
problems 2--6 on
thermodynamics and
blackbody radiation.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 7.
Question: Recalling the
Stefan-Boltzmann law F = σT**4,
say one increases temperature of a
blackbody radiator by a factor of 2.
Answer 4 is right.
F_2 = σT_2**4 = σ(2T_1)**4=σ(2**4 * T_1**4) = 16 * F_1 .
Group Activity:
Line spectra are usually created by diffraction gratings. How diffraction gratings work is explicated in the figure below (local link / general link: diffraction_grating.html).
For an example of a line spectrum,
see the figure below
(local link /
general link: line_spectrum_iron.html).
The study of line spectra
is called spectroscopy.
Why are there line spectra what kinds are there, and what can we do with them? We explicate in the subsections below.
Quantum mechanics explains why atoms, molecules, and ions have spectral lines.
An atomic transitions/molecular transition is a change in the internal energy state of the atoms, molecules, or ions.
These energy states have only certain discrete energy values: they are QUANTIZED.
To conserve energy, energy must be emitted or absorbed during transition.
The energy change can only come in set of quantized values depending on the quantized states.
Emitting or absorbing EMR in photons is one possible way of conserving energy.
Thus, emitted photons have quantized energy values which give the spectral lines.
A longer explication is given in the figure below (local link / general link: atom_diagram_abstract.html).
If you just have a hot, dilute gas then usually you will see an
emission line spectrum
from photons from the
spectral lines of
atoms,
molecules,
and/or
ions.
The line spectra
of a species is nearly unique and has become the most important identifier
of that species in
modern science.
The study of line spectra
is spectroscopy.
Spectroscopy is the most
important of all chemical analysis tools---it tells us what matter is made of.
It is vastly easier than doing chemical reactions
for chemical analysis.
And you don't have to have the matter in your hand---you just need
line spectrum from
the matter---either an emission line spectrum
or an absorption line spectrum
(see subsection
Above the Stellar Photosphere is the Stellar Atmosphere below).
Spectroscopy tells us what
observable universe is
made of---without leaving Earth.
A continuous spectrum
and a emission line spectrum
are compared in the figure below
(local link /
general link: spectrum_emission_line_cartoon.html).
But for an
line spectrum
you don't see a long band of colors gradually changing;
you see just isolated strips (i.e., lines) of colors surrounded by
relative darkness.
Some example atomic
line spectra
and some star
absorption line spectra
are shown in the figure below
(local link /
general link: nasa_spectra.html).
We explain absorption line spectra
in subsection
Above the Stellar Photosphere is the Stellar Atmosphere below.
Spectral lines
are so called because the EMR they emit
when dispersed through a device with a slit aperture,
gives rise to lines in the spectrum.
As well as identifying the
atoms,
molecules,
and/or
ions,
one can
also usually learn something about their abundances, and the
temperature
and density of a gas from
spectroscopy
plus modeling.
To reiterate: It is true to say that
spectroscopy
is the most important chemical analysis technique of all.
You do NOT need a sample of a substance in your hand. You just need
light from a hot low-density gas
source containing the substance.
The light
could be from all across the observable universe.
The ability to chemically analyze without having a sample in hand was NOT
anticipated historically as discussed in the figure below
(local link /
general link: auguste_comte.html).
In many cases, just by looking at the
line spectrum
from a gas many
of the constituent
atoms,
molecules,
and/or
ions
can be identified BY EYE
by experienced spectroscopists.
Yours truly is sort of a spectroscopist himself---but
evidently NOT a good
one since yours truly can't do this---except in very easy cases.
A line spectrum
can be created and studied using a spectroscope
(see the figure below:
local link /
general link: spectroscope.html)
which is just
a device that disperses light
into a spectrum.
Question: Emission line spectra
are called emission line spectra because:
A recapitulation of the explanation of
the formation of emission line spectra
is given in Emission spectrum of hydrogen | 0:57
in
Spectroscopy videos
below
(local link /
general link: spectroscopy_videos.html).
Answer 2 is right.
EOF
Also one can determine the source's velocity relative
to the observer along the line of
sight. This makes use of the Doppler effect
which is
discussed below in the section The Doppler Effect.
Form groups of 2 or 3---NOT more---and tackle Homework 7 problems 2--7 on thermodynamics, blackbody radiation, and line spectra.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 7.
We answer in a few subsections below:
The EMR in the deep interior of a star is forced by high local opacity to be in thermodynamic equilibrium with its local environment: i.e., it has a blackbody spectrum with a temperature equal to that of the local matter.
The interior is very hot with matter with temperatures typically rising from tens of thousands of degrees at the photosphere and reaching of tens of millions of degrees in the center. So typically in the deeper interior, the EMR's blackbody spectrum has a maximum in or near the X-ray band (fiducial range 0.1--100 Å) (HRW-802). Recall Wien's law λ_max = 2.8977729(17) Å*K/(T/10**7).
But EMR from the deep interior does NOT escape the star. The photons that are emitted are absorbed after a short distance by matter.
As discussed in IAL 6: Light and Electromagnetic Radiation (EMR) one can picture the EMR as photons on a random walk from the interior to the outside (see the figure below: local link / general link: photon_escape.html). This is an important example of heat energy flowing from hot to cold.
In a random walk, photons are emitted in random directions from matter, travel some distance often scattering off atoms or free electrons, and then are absorbed.
Their energy is then re-emitted as other photons, but at temperature corresponding to the matter where they are re-emitted from.
The temperature, density, and opaqueness of a star decrease going outward. This gives a bias for longer flights in the outward direction. Near the surface the photons come from relatively low temperatures compared to the interior.
As the photons
random walk
out from the interior of a star,
finally there is layer where the density is so low
that outward going
photons
can escape to infinity at least about half the time.
We call this layer the
photosphere.
See the figure above.
The photosphere
is the layer from which we see most
EMR coming from the star.
The photosphere
often called the surface of the star.
But, in fact, stars have no definite surface.
Their density decreases going outward and probably becomes
negligibly small at some point, but without a sharp cut-off.
Many stars
are probably like the Sun whose atmosphere extends into
a solar wind
where matter is blowing off the Sun.
This wind extends outward until it merges with the
interstellar medium (ISM).
The
photosphere
is layer NOT exactly at a single temperature.
Thus you will get a continuous spectrum
from the photosphere
that
is a mixture of blackbody spectra at slightly different temperatures.
Nevertheless, you can often fit the
photosphere
spectrum by a
blackbody spectrum
at a single temperature to high accuracy.
Although the photons
can escape at most wavelengths from the
photosphere,
the lines of
atoms,
molecules,
and/or
ions
are particularly
strong absorbers even when continuum absorption has grown weak because
of low density.
So above the
photosphere
in what is called the stellar atmosphere,
the lines will absorb some of the
continuous spectrum
in the narrow wavelength bands corresponding to the lines.
They absorb because the atoms, etc., are colder than the
EMR from
the photosphere.
This line-absorbed EMR
is reprocessed into some other form of energy which eventually
escapes the star
are as EMR,
but mostly NOT in the wavelength bands were it was absorbed.
The absorption by the lines creates an
absorption line spectrum:
a bright continuous spectrum
with superimposed dark absorption lines.
The figure below
(local link /
general link: spectrum_formation.html)
illustrates
how absorption line spectra
are formed.
An example
of an absorption line spectrum
is our old friend the
solar spectrum.
Let's first look at solar spectrum
in image represention
(which one gets directly from
dispersion
by diffraction grating)
in the two figures below
(local link /
general link: solar_spectrum_image.html;
local link /
general link: fraunhofer_lines.html).
The figure below
(local link /
general link: spectrum_formation_stellar.html)
illustrates
how absorption line spectra
are formed in stars
and shows a cartoon of an
absorption line spectrum in
intensity representation.
A recapitulation of the explanation of
the formation of absorption line spectra
is given in the video
Spectrum of the Stars | 0:54
in Spectroscopy videos
below
(local link /
general link: spectroscopy_videos.html).
EOF
In the figure below
(local link /
general link: solar_spectrum_graph_2.html)
is a graph
of the solar spectrum
in
flux representation.
It is a log-log plot
with a wavelength scale
too coarse to show individual
absorption lines.
Hereafter, for brevity, we will usually just refer to the two cases specified above as mechanical waves and EMR.
The Doppler effect is somewhat similar in the two cases, but the detailed behavior and the formulae are different in general as noted above.
The
Doppler effect
was first discovered by Austrian
Christian Doppler (1803--1853)
in 1842 for
light.
The application to sound came only a little later in about
1845.
The Doppler effect
for sound is, in fact, an
everyday-life
phenomenon.
Pitch
is the human
psychoacoustical perception of
sound frequency plus other sound features to a lesser
degree.
We notice that the pitch
of a
siren
or aircraft
changes noticeably as those pass you---from high to low---and so
we notice the Doppler effect.
The Doppler effect
for
electromagnetic radiation
turns up in everyday life with
police radar guns
which are used to judge relative speeds and
catch speeders.
Understanding the Doppler effect
for mechanical waves
(i.e., for where there is a medium:
e.g., sound waves
and waves on a string)
in the classical limit
is easy qualitatively
and NOT so hard quantitatively.
An explication is given in the figure below
(local link /
general link: wave_propagation.html).
We explicate the
Doppler effect for
electromagnetic radiation (EMR)
in vacuum in the figure below
(local link /
general link: doppler_effect_relativistic.html).
Now for the Doppler effect
in astronomy.
Note continuous spectra
have an infinite range of behavior.
So you CANNOT just try a finite set of
articially shifted
continuous spectra
to get a fit an observed data.
Note also continuous spectra
are generally NOT pure
blackbody spectra,
and even if you knew one was
a pure blackbody spectrum,
you would NOT in general know the source's temperature.
Note finally that even if you knew the intrinsic
continuous spectrum
of particular astro-body,
that continuous spectrum
can be modified by transmission through the
interstellar medium (ISM)
in a generally unknown way.
The upshot is that
continuous spectra
are usually NOT too useful in determining radial velocities of
astro-bodies.
On the other hand, making use of
line spectra
to determine radial velocities
is very easy as explicated illustrated
in the figure below
(local link /
general link: doppler_effect_line_spectra.html).
There are two similar wavelength shifting effects,
that are often called
Doppler shifts, that turn up in astronomy:
A comparison of the
Doppler effect
and the cosmological redshift
is given in the figure below
(local link /
general link: cosmological_redshift_doppler_shift.html).
With the spread of trains and
train whistles in the
1840s,
the Doppler effect
for sound probably became pretty obvious.
The Doppler effect
for sound
is also used by bats---see
the figure below
(local link /
general link: doppler_effect_bat.html).
The 3 figures below
(local link /
general link: doppler_effect_siren_animation.html;
local link /
general link: doppler_effect_spherical_waves.html;
local link /
general link: doppler_effect_sonic.html)
further illustrate how
the Doppler effect arises
for mechanical wave
in the classical limit---it's
really very easy to understand qualitatively.
Question: Why is the
Doppler effect
of interest in astronomy?
Answer 1 is right.
Question: The
Doppler effect
in astronomy is most useful for:
You CANNOT know the shift of an observed
continuous spectrum,
unless you know what the emitted spectrum was like in its own
rest frame and usually you do NOT know that until after you
have determined the relative velocity.
Answer 3 is right.
Some---like yours truly---consider it a mistake to call these effects the
Doppler effect though
they are related effects.
Others are more relaxed about the use of the
expression Doppler effect
and say both those wavelength shifts are
a Doppler effect.
Form groups of 2 or 3---NOT more---and tackle Homework 7 problems 8--14 (omitting 11) on stellar spectra, blackbody radiation, and the Doppler effect.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 7.
