Gustav Robert Kirchhoff (1824-1887)
Law #1: Kirchhoff's heat radiation law. Heat radiation, also called thermal radiation, is the radiant energy an object emits by virtue of its temperature. Heat radiation is all around us in the form of very low-power electromagnetic waves emitted by room-temperature or outdoor-temperature objects in the microwave and infrared regions of the spectrum. This radiation is invisible to us, but can be felt, for instance, as heat from pavement, brick, and car bodies and interiors, heated by the sun during the day. This is purely electromagnetic energy being absorbed, increasing the average kinetic energy (temperature) of the atoms that make up the object, then being converted into purely electromagnetic energy emitted by the object.
When is heat radiation visible? When an object can be heated until it glows. This is called incandescence: part of the heat radiation is in the visible spectrm. If the object glows really brightly, it can be used as a source of light to see other objects, so this is a second way we see heat radiation: when it is reflected from all the things we're able to see when they're illuminated by a source of thermal radiation.
Many of the materials we see around us such as wood, cloth, plants, etc, cannot withstand temperatures high enough to make them incandescent, because they would catch on fire, and the light emitted by fire isn't heat radiation. But certain types of material--metal and glass, for instance--can be heated enough to emit a reddish glow without combusting or incinerating.
Besides molten metal and molten glass, which we don't have the opportunity to observe very often (ditto lava), the common examples of incandescence we see are the burners on electric stoves (~1500° F), the tungsten filaments of incandescent bulbs (~2500° F), and the sun and other stars. The sun has a surface (photosphere) temperature of about 10,000° F. Bigger, hotter stars range up to 90,000 degrees for their photosphere temperatures. (The cores of stars have temperatures in the millions of degrees.)
Warm-blooded animals also produce heat radiation. A person actually emits about as much heat radiation as a 100-watt incandescent bulb (2200 kilocalories/day ≈ 100 joules/sec = 100 watts). The difference is in the intensity of the radiation being emitted, measured in power per unit area. The watts per square centimeter that you are constantly emitting is fairly low, but if you multiply it by the area of your skin in square centimeters, you get approximately 100 watts.
Sources of visible light that are not incandescent are called luminescent. This screen you're looking at is luminescent. Fluorescent lights, gas discharge tubes (neon lights, for instance), LEDs, and phosphorescent objects that glow greenly in the dark are just a few examples of luminescence.
The objects I've mentioned that produce their own thermal radiation from an external or internal energy source--electric stove heating elements, incandescent light bulbs, stars, and people--are not in thermodynamic equilibrium with their surroundings, because they aren't continually absorbing as well as emitting thermal radiation. In contrast, objects that are not sources of energy are emitting thermal radiation because they are also absorbing thermal radiation from their environment, and there is equal absorption and emission. The examples I mentioned above are pavement, manhole covers, and cars that heat up because they absorb sunlight.
---------
Okay, finally, we're about to get to Kirchhoff's almost-famous law of thermal radiation. Consider this: In the most general case, light can be reflected, absorbed, or transmitted when it hits a material surface such as metal or glass. Usually, however, metals don't transmit any light (it's reflected or absorbed) and glass doesn't absorb any light (it's reflected or transmitted). But you probably know glass absorbs some of the ultraviolet light that hits it (no sunburn through windows), and you probably don't know that a very, very thin piece of metal can actually transmit light (Ernest Rutherford's gold foil was that thin). For a piece of metal of normal thickness, however, light can only be reflected or absorbed. That's the general case for material objects: some reflection, some absorption.Reflectivity ʀ and absorptivity Aν are the fractions of the incoming light hitting a surface that are reflected and absorbed, respectively. For non-transmitting material, they add to one, unity, 1, numero uno, because the light has no other place to go when it can't be transmitted through the material. The portion of the incoming light that isn't reflected is absorbed and heats up the material. The heated material emits thermal radiation.
For a mirror--a flat, clear piece of glass with a thin coating of aluminum or silver on the back-- ʀ is very close to 1, so there's very little absorption in the visible light region. The mirror is not going to heat up if you put it out in the sun. The other extreme is out on the streets in the form of asphalt and iron manhole covers. You know they get hot as hell in the summer sun! This is because there's a lot of absorption and consequent emission, especially in the infrared region, plus some diffuse reflection in the visible region (you can see them as distinguishable objects or materials). Now we jump into a sort of formal discussion of Kirchhoff's heat radiation law.
"According to Kirchhoff’s law of heat radiation, the ratio of the emissive power Eν to absorptive power Aν of a body depends only on the frequency ν and on the temperature T of the body and not on the nature of the body, i.e.
Eν / Aν = K (ν,
T),
where K (ν, T) is a universal function of ν and
T.”
This sentence comes from Chapter 14 of Born & Wolf’s Principles
of Optics, 7th edition, fifth printing (2009), pages 747 and 748. The chapter title is “Optics of Metals". The "universal" nature of K (ν, T) is that it doesn't depend on the material, which at first seems rather miraculous. I mean, does styrofoam (polystyrene foam) actually obey this law? Yes, but only within a limited range of frequencies, and at temperatures that are low enough to keep it from going up in smoke, and its absorptive power is very small. Metals (gold, silver, and copper for instance), besides being the best electrical conductors and best absorbers and emitters of radiation, have the widest frequency and temperature range within which they remain solids or liquids and don't get vaporized. Thus we find Kirchhoff's law discussed in the B&W chapter on metals.
They explain in a footnote on page 747 that emissive power is “the radiant energy
emitted by the body per unit time,” and absorptive power is “the fraction which
the body absorbs of the radiant energy falling upon it.” So emissive power is in units of power
(watts, for instance), and the absorptive “power” is just a ratio, a
dimensionless number between zero and one.
But what about metals being good reflectors of radiation? Well, highly reflective metallic surfaces perform absorption and re-emission of light at their surfaces so quickly that they don't heat up, and the process of rapid absorption and re-emission is called reflection. Thus some metals are not good absorbers of visible radiation in the sense of Kirchhoff's radiation law, but their ratio of emissive power to absorptive power still follows the universal Kirchhoff formula.
Absorptive power is really a measure of how much incident radiation is converted into heat in the material, and emissive power is measure of how much heat is converted into radiation. So Kirchhoff's law of heat radiation when viewed and stated in this manner seems obvious rather than miraculous: a poor absorber of radiation is a poor emitter, and a good absorber is a good emitter.
But what about metals being good reflectors of radiation? Well, highly reflective metallic surfaces perform absorption and re-emission of light at their surfaces so quickly that they don't heat up, and the process of rapid absorption and re-emission is called reflection. Thus some metals are not good absorbers of visible radiation in the sense of Kirchhoff's radiation law, but their ratio of emissive power to absorptive power still follows the universal Kirchhoff formula.
Absorptive power is really a measure of how much incident radiation is converted into heat in the material, and emissive power is measure of how much heat is converted into radiation. So Kirchhoff's law of heat radiation when viewed and stated in this manner seems obvious rather than miraculous: a poor absorber of radiation is a poor emitter, and a good absorber is a good emitter.
--------
Planck referred to Kirchhoff’s heat radiation law as a proportionality, so let’s just write it
that way:
Eν = Aν K (ν,
T)
If Aν is considered constant (not usually the case) over the range of frequencies and temperatures of interest in an experiment, this is a proportionality of emission rate to K (ν, T). Going one step further and taking the absorptive power of a body for all electromagnetic frequencies as Aν = 1, we have the idealized concept of a black-body: an object
or surface that absorbs all the radiant energy that hits it, and emits this energy as radiation that follows the frequency-dependent and temperature-dependent family of curves given by K (υ, T), which is the formerly-much-sought-after universal function that Planck discovered in December 1900 by using the idea of what came to be called quantum energy elements.
Charcoal is one familiar substance that comes close to being an ideal black-body, but no actual material surfaces (not even pieces of metal covered with soot) fit the black-body curve perfectly. Ideal black-body radiation is emitted from an empty metal box, or cavity in a metal block, with a small hole in it.
The radiation in the cavity is only what is being constantly emitted and absorbed by the walls of the cavity held at a given temperature T, and this includes the small amount of radiation entering from the little hole. All the radiation entering the hole is absorbed by it: the hole is a perfect absorber of radiation. Being a perfect absorber, the hole also is a perfect emitter. What is observed coming out of the hole is a small sample of the equilibrium radiation within the cavity, and the hole is thus an ideal source of black-body radiation.
The other five laws
Kirchhoff's voltage and current laws: Kirchhoff also has two circuit laws or rules, and these are the laws I first saw his name attached to, since I studied electronics before ever taking a physics course. The voltage law says the sum of voltages on circuit components connected in a closed loop is zero. The current law says the sum of currents into a circuit junction is zero. In both cases, the negative contributions cancel the positive contributions. These laws are really just rules that are consequences of the laws of conservation of energy (in the voltage law case), and the conservation of electric charge (in the current law case).
Kirchhoff's three spectroscopy laws: And then, finally, there are Kirchhoff's laws related to spectroscopy, which are discussed in the astronomy textbook Introductory Astronomy and Astrophysics by Elske v. P. Smith and Kenneth Jacobs, first published in 1973 and used by Prof. G. Stanley Brown for the intermediate astronomy class at UALR I took in the spring of 1977, when I was also observatory assistant to Dr. Brown at the observatory on public nights:
Kirchhoff's three spectroscopy laws: And then, finally, there are Kirchhoff's laws related to spectroscopy, which are discussed in the astronomy textbook Introductory Astronomy and Astrophysics by Elske v. P. Smith and Kenneth Jacobs, first published in 1973 and used by Prof. G. Stanley Brown for the intermediate astronomy class at UALR I took in the spring of 1977, when I was also observatory assistant to Dr. Brown at the observatory on public nights:
“Sir Isaac Newton showed how light could be dispersed
into a rainbow-hued spectrum, and Gustav
Kirchhoff (1824-1887) in 1859 stated his three empirical rules or ‘laws’
relating light spectra to their material source:
(1) a solid, a liquid, or a gas under high pressure,
when heated to incandescence, will produce a continuous spectrum;
(2) a gas under low pressure, but at sufficiently high
temperature, will give a spectrum of bright
emission lines; and
(3) a gas at low pressure (and low temperature), lying
between a hot continuum source and the observer, causes an absorption line spectrum, i.e., a number of dark lines superimposed
on the continuous spectrum.
Although Kirchhoff’s laws simply describe spectral
phenomena, and are incomplete as written in the preceding paragraph, the
recognition that exactly the same spectral lines appeared when a given gas
(e,g., oxygen) was used in experiments (2) and (3) provided the Rosetta Stone
of stellar astronomy. Each element has
its own characteristic set of spectral lines.
By comparing laboratory and stellar spectra, men like Joseph Fraunhoffer
(1787-1826), Kirchhoff, and Sir William Huggins (1824-1910) could deduce
the presence of certain elements in stars.
The way was now open for an astrophysical interpretation of the
compositions and properties of the distant stars.”
------
--------
----------
--------------
--------------
And a final word on Kirchhoff's heat radiation law that I started with: This is (1), above, for which we have approximate black-body radiation produced by the thermal energy emitted by solids, liquids and gases, examples of which I mentioned near the beginning of this post. The variation of Aν with frequency is what makes these objects not produce an Eν curve with the same shape as the perfect Planckian black-body curve K (ν, T), for which Aν = 1 for all frequencies.
