The Physics
Opus in profectus


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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, 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".

stefan-boltzmann law

Hot objects are "brighter" than cold objects. Dark objects are 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.

Φ = εσA(T4 − T04)


Φ =  (phi) 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 = 
5k4  =  π2k4
15h3c2 60ℏ3c2
σ =  5(1.38× 10−23 J/K)4
15(6.63 × 10−34 Js)3(3.00 × 108 m/s)2
σ =  5.67 × 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. (Source: NARA)

Disconnected thoughts that aren't quotes.

wien's displacement law

Warm objects are infrared, warmer objects are red hot, even warmer objects are white hot, even more warmer objects are blue hot. Color and temperature are related.

Wien's displacement law relates the peak wavelength of the thermal radiation emitted by an object to its absolute temperature. First derived by the German physicist Wilhelm Wien in 1893 from a difficult thermodynamic argument that I will not pretend to understand; now derived mathematically from Planck's law.

λmax =  hc   1
k xT

where x is the solution of…

xex  − 5 = 0
ex − 1

x = 4.96511…

In shortened form…

λmax = b


λmax =  (lambda max) the peak wavelength [mm] of the emitted thermal radiation
b =  Wien's displacement constant, 2.898 mmK
T =  the absolute surface temperature [K] of the object emitting thermal radiation

A more complete explanation of this law can be found in the section on Planck's law.

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solar energy

greenhouse effect


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

Other naturally occurring greenhouse gases of lesser concern.

Greenhouse gases that do not occur naturally.

Indirect greenhouse gases

key infrared absorption bands in the atmosphere correspond to H2O, CO2, O3

Global warming properties of selected greeenhouse gases Source: IPCC and others, * trifluoromethyl sulphur pentafluoride
molecule global warming
(CO2 = 1)
CO2 carbon dioxide 1 120 1.66 0.000014
CH4 methane 21 12 0.48 0.00037
N2O nitrous oxide 310 114 0.16 0.00303
CCl3F CFC-11 3,800 45 0.063 0.25
CF2Cl2 CFC-12 8,100 100 0.17 0.32
C2F3Cl3 CFC-113 4,800 85 0.024 0.3
CHClF2 HCFC-22 1,500 12 0.033 0.2
CCl4 carbon tetrachloride 1,400 26 0.012 0.13
CH3CCl3 methyl chloroform 146 5 0.0011 0.06
CHF3 HFC-23 11,700 270 0.0033 0.19
C2HF5 HFC-125 2,800 29 0.0009 0.23
C2H2F4 HFC-134a 1,300 14 0.0055 0.16
C2H4F2 HFC-152a 140 1.4 0.0004 0.09
SF6 sulfur hexafluoride 23,900 3,200 0.0029 0.52
SF5CF3 see note below* 19,000 1,000 ? 0.59
H2O water, tropospheric ? ? ? ?
H2O water, stratospheric ? ? 0.02 ?
O3 ozone, tropospheric ? ? +0.35 ?
O3 ozone, stratospheric ? ? −0.15 ?
CO carbon monoxide ? 0.25 ? ?
H2 hydrogen ? ? ? ?

Temperatures are rising across the globe.