Heat radiation (as opposed to particle radiation) is the transfer of internal energy in the form of electromagnetic waves. For most bodies on the Earth, this radiation lies in the infrared region of the electromagnetic spectrum.
One of the first to recognize that heat radiation is related to light was the English astronomer William Herschel (1738–1822), who noticed in 1800 that if a thermometer was moved from one end of a prism produced spectrum to the other, the highest temperatures would register below the red band, where no light was visible. Because of this position, this form of radiation is called infrared (infra being the Latin word for below or within). Sometimes this kind of radiation is called "heat waves" but this is a misnomer. Recall that heat is the transfer of internal energy from one region to another. As all forms of electromagnetic radiation transfer internal energy, they could all be called "heat waves".
Hot objects are "brighter" than cold objects. Dark objects lose and gain heat faster than light objects.
The Stefan-Boltzmann law relates the heat flow rate emitted or absorbed from an object to its temperature (and surface area and darkness). It was empirically derived by the Austrian physicist Joseph Stefan in 1879 and theoretically derived by the Austrian physicist Ludwig Boltzmann in 1884. It is now derived mathematically from Planck's law.
P = εσA(T4 − T04)
|P =||net heat flow rate [W] emitted (+) or absorbed (−)|
|ε =||(epsilon) emissivity, a dimensionless (unitless) measure of a material's effective ability to emit or absorb thermal radiation from its surface; ranges from 0 (none) to 1 (maximal)|
|σ =||(sigma) Stefan's constant, 5.670 × 10−8 W/m2K4|
|A =||surface area [m2] of the object emitting or absorbing thermal radiation|
|T =||absolute temperature [K] of the object emitting or absorbing thermal radiation|
|T0 =||absolute temperature [K] of the environment|
Connect Stefan-Boltzmann law to Planck's law.
|σ =||2π5(1.38 × 10−23 J/K)4|
|15(6.63 × 10−34 J s)3(3.00 × 108 m/s)2|
|σ =||5.670374419 × 10−8 W/m2K4|
Dark colors absorb more radiant energy than do light colors. The burns on this woman's skin mimic the pattern on her blouse. She was exposed to a monstrous dose of electromagnetic radiation from a nuclear blast.
Disconnected thoughts that aren't quotes.
- blackbody radiation, cavity radiator, the Sun is a blackbody
- For humans, the emissivity in the infrared region is independent of the color of the skin and is nearly equal to 1, indicating that the skin is almost a perfect absorber and emitter of radiation at this wavelength. If we could see in the deep infrared emitted by the body we would all be nearly black. Under normal conditions, about half our energy loss is through radiation, even if the surrounding environment is not much lower than body temperature.
- Thermos Flask, invented by James Dewar, Scotland. Coating the inside of an evacuated double walled, glass bottle with a thin layer of silver reduced the heat loss by radiation by a factor of 13. Dewar commissioned a German glass blower to make some, who discovered that milk for his baby stayed warm in the flask overnight. He took the idea of the "Thermos Flasche" to a manufacturer.
- A glass cake pan will require 20% less baking time than a shiny surfaced pan.
Wien's displacement law
Warm objects are infrared, warmer objects are red hot, even warmer objects are white hot, even more warmerer objects are blue hot. Color and temperature are related or more precisely, spectra and temperature are related. The absolute temperature of an object emitting thermal radiation is inversely proportional to the peak wavelength of its spectrum and directly proportional to the peak frequency of its spectrum.
These relationships became know as Wien's displacement law to honor the German physicist Wilhelm Wien who first formulated the law in 1893. Wien used a difficult thermodynamic argument that I will not pretend to understand. The law is now derived mathematically from Planck's law and is done so more formally in that section of this book.
The law was originally stated in terms of peak wavelength.
|λmax =||the peak wavelength in the spectrum of the thermal radiation emitted by an object (read the symbol as "lambda max")|
|b =||Wien's displacement constant (sometimes called Wien's wavelength displacement constant). The choice of units depends on the nature of the radiation being studied. The SI unit of wavelength is the meter, but use whatever unit you prefer for whatever application you have to deal with.
|T =||the absolute surface temperature [K] of the radiating object|
Wien's law now is sometimes also stated in terms of peak frequency.
fmax = b′T
|fmax =||the peak frequency in the spectrum of the thermal radiation emitted by an object|
|b′ =||Wien's frequency displacement constant (read the symbol as "bee prime"). Again, the choice of units depends on the situation. The SI units is the hertz, but I prefer the gigahertz for peaks in the microwave bands (like the cosmic microwave back ground) and terahertz for peaks in the infrared and visible bands (which is pretty much everything else).
|T =||the absolute surface temperature, in kelvin [K], of the radiating object|
Please note that the two constants are not interconvertable using the wave speed equation. These equations are true…
|⇔||c = fλ||⇔||
but these equations are inequalities…
|⇔||c ≠ fmaxλmax||⇔||
The constants in Wien's displacement law are derived from spectral distributions over wavelength and frequency — basically, complicated probability distributions. Although wavelength and frequency are inversely proportional, their behavior as variables in spectral distributions do not transform so easily.
Try these simple comparisons. Determine the peak wavelength and frequency for the thermal radiation coming from the Sun (T = 5772 K). Using your favorite reference source determine the type of radiation and its color if it is visible.
|fmax = b′T|
|fmax = (0.0587926 THz/K)(5772 K)|
|fmax = 339 THz|
The peak wavelength, 502 nm, is in the green part of the visible spectrum — although in some cultures this wavelength might be considered blue. The peak frequency, 339 THz, is in the infrared — that statement is true for all human cultures.
Let's now do the naive transformations for a less subjective comparison. The numbers just don't work out.
|blackbody color by temperature|
|radiant energy source|
|2.73||cosmic background radiation|
|500||household oven at its hottest|
|660||minimum temperature for incandescence|
|770||dull red heat|
|1,400||glowing coals, electric stove, electric toaster|
|2,800||incandescent light bulb, 75 W|
|2,900||incandescent light bulb, 100 W|
|3,000||incandescent light bulb, 200 W|
|3,100||sunrise or sunset (effective)|
|3,200||professional studio lights|
|3,600||one hour after sunrise or one hour before sunset (effective)|
|4,000||two hours after sunrise or two hours before sunset (effective)|
|5,500||direct midday sunlight|
|7,000||overcast sky (effective)|
|incipient red heat||500–550||770–820|
|dark red heat||650–750||0920–1020|
|bright red heat||850–950||1120–1220|
|yellowish red heat||1050–1150||1320–1420|
|incipient white heat||1250–1350||1520–1620|
|T (K)||class||λmax (nm)||color name||examples|
|6000||G||480||yellow||Sun, Alpha Centauri|
- The total global energy consumption of all the humans on the planet is about 1.4 × 1013 W or about one ten-thousandth the total energy from the Sun incident on the Earth. The energy use per area in US metropolitan areas is roughly 2% of the incident solar energy.
- 3.828 × 1026 W total solar luminosity
1361 W/m2 solar constant (energy perpendicular to direction of propagation)
0.297 albedo (latin albus, white), surface 0.04, atmosphere 0.26
340 W/m2 effective solar constant (averaged over time and surface)
- Arrhenius 1896 estimates CO2 warming
- Keeling 1960 shows CO2 is increasing
- Manabe 1967 develop radiative convective model, first GCM
- Hansen 1988 GCMs indicate the signal of anthropogenic global climate warming would soon emerge from natural variability
- Ice cores
- Mann 1998 Hockey stick graph
The basic effect…
Global temperature and atmospheric carbon dioxide trends match. The very long graph made popular by Al Gore in An Inconvenient Truth.
Plot one against the other. The relation is approximately linear. Al Gore never did this one.
Naturally occurring greenhouse gases whose concentrations are increasing due to human activities
- CO2 from burning forests and fossil fuels
- CH4 from rice paddies, cattle, termites (whose population is thought to have increased due to global deforestation), oil fields, and pipeline leaks
- N2O of agricultural origin
Other naturally occurring greenhouse gases of lesser concern.
- Water is also a greenhouse gas, but its concentration in the atmosphere is affected by temperature and is not directly affected by human activities.
- Ozone is also a greenhouse gas but its greenhouse effects are not easily quantified
Greenhouse gases that do not occur naturally.
- CFCs from from discarded or leaky refrigerators and air conditioners
Chlorofluorocarbons (CFCs) do not exist naturally, but were invented in the 1930s by researchers at General Motors looking to replace the toxic and corrosive refrigerants in use at the tine: ammonia and sulfur dioxide. CFCs are also implicated in stratospheric ozone loss (the so called "hole" in the ozone layer).
- HFCs, hydrofluorocarbons
- HCFCs, hydrocholofluorocarbons
- PFCs, perfluorocarbons
Indirect greenhouse gases
- carbon monoxide
key infrared absorption bands in the atmosphere correspond to H2O, CO2, O3
(CO2 = 1)
|SF5CF3||see note below*||19,000||1,000||?||0.59|
Carbon dioxide levels are rising.
Temperatures are rising across the globe.
But especially in and near the Arctic.