Notes
The rate at which energy is emitted at all wavelengths by such a body per square meter is called its radiant flux. The radiant flux increases with temperature (think of hot coals: dull red if not too hot, much brighter/whiter if you blow on them). The precise dependence of radiant flux on temperatue is given by the Stefan-Boltzmann law (1855): radiant flux is \(\sigma T^4\), where the constant \(\sigma\) is about
The amount of energy emitted by body per unit time is its radiant flux multiplied by its surface area. Energy per unit time has the units of power, measured in watts. The radiant energy per unit time emitted by a spherical body of radius \(R\) is therefore
The solar flux (incoming energy) at the radius of the Earth’s orbit is \(S = 1.37\) kilowatts per square meter. We now ask: how much of that incoming energy is absorbed by the Earth? We know that certain fraction is reflected back into space, while the rest is absorbed. Let \(\alpha\) be the fraction of the energy whih is reflected. This is called the albedo. The albedo of the Earth as a whole epends on cloud cover, the extent of the polar ice caps, etc., but is presently about \(0.3\).
Carbon dioxide
Is Carbon Dioxide Opaque to Infrared Radiation?
Short answer: yes — carbon dioxide (CO₂) is opaque to some infrared (IR) radiation, but not to all of it.
What “opaque” means in this context
CO₂ is selectively opaque in the infrared.
It absorbs IR radiation only at specific wavelengths, corresponding to particular molecular vibrational modes.
So:
- ❌ It is not opaque to all infrared radiation
- ✅ It is strongly opaque at certain infrared bands
The key absorption bands
The most important absorption band for CO₂ is centered around:
- ≈ 15 micrometers (µm)
This is crucial because Earth, at an average temperature of about 288 K, emits a large fraction of its thermal (blackbody) radiation near this wavelength.
CO₂ also has a strong absorption band near 4.3 µm, but this lies closer to the Wien tail of Earth’s emission and is less important for climate.
Why CO₂ absorbs infrared radiation
CO₂ is a linear triatomic molecule.
Certain vibrational modes—especially bending modes—produce a changing electric dipole moment. These modes are therefore infrared-active.
When an IR photon of the right wavelength encounters a CO₂ molecule:
- The photon is absorbed
- The molecule vibrates
- The energy is later re-emitted (in a random direction) or transferred to surrounding molecules via collisions
This microscopic process underlies the greenhouse effect.
An important nuance
CO₂ does not: - trap heat like a physical blanket - absorb visible sunlight efficiently - block all outgoing radiation
Instead, it: - reduces the transparency of the atmosphere at specific IR wavelengths - raises the effective altitude from which Earth radiates energy to space - thereby alters the planet’s radiative energy balance
One precise summary sentence
Carbon dioxide is opaque to infrared radiation at specific wavelengths—most notably near 15 µm—making it a key contributor to Earth’s greenhouse effect.