Wuwei
Gold Member
- Apr 18, 2015
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Some people, including the infamous Dr. Happer say that CO2 cannot radiate due to a plethora of molecular collisions that abort almost all of the ability to radiate15 micron photons. Why are they wrong?
The short answer:
A molecule vibrating in the15 micron radiation mode can hold that energy for 0.335 seconds.
The number of molecular collisions during that time is over a billion. However the vast majority of those collisions will simply bounce off without changing the molecular vibration state. Because of that, almost all CO2 molecules will keep their energy until they emit 15 micron radiation into the atmosphere.
The long answer:
These are the details of the short answer:
https://apps.dtic.mil/dtic/tr/fulltext/u2/771554.pdf from Table V
The average lifetime of a CO2 molecule in a bending vibration mode (15 micron radiation wavelength)
is 0.335 seconds.
Frequency of Molecular Collisions
The average atmospheric molecular collision frequency is 3.25×10⁹ collisions/second.
If just one of those billions of collisions were able to quench the CO2 vibrations, the probability of a CO2 radiating would be roughly 1 / 3.25×10⁹x0.335 which is 1 in 1.09 billion.
At first sight it would seem that the collision rate is so high that, for practical purposes all radiation vanishes. However inelastic collisions that would quench a CO2 vibration state are rare. Elastic collisions simply bounce off without changing any internal energy and are predominant.
https://pure.tue.nl/ws/files/3478579/109243.pdf “On Vibrational Relaxations in Carbon Dioxide”
TABLE III Translational Transition Probabilities Page 33.
This table gives the probabilities that a collision will quench a CO2 molecule in a 15 micron bending mode. The second column shows the probability is Pd² = 2.0 10⁻¹³ at 300 K. An extrapolation to the global average temperature of 288 K temperature gives a quenching collision probability = 1.7×10⁻¹³. That probability is very small.
Number of CO2 molecules per m³ @ 400ppm = 1.01×10²².
The number of atmospheric CO2 molecules in a 15 micron excitation state is
1.01×10²² x 2/9 = 0.244×10²² (2/9 comes from Equipartition Principle)
The probability that a single collision will quench that excited state = 1.7×10⁻¹³
The probability that a single collision does not quench the excited state = (1- 1.7×10⁻¹³)
The probability that none of the 1.09 billion collisions quenches the excited state =
(1 − 1.7×10⁻¹³)^1.09×10⁶ ≅ 1 − 1.7×10⁻¹³ × 1.09×10⁶ = 1 − 1.853×10⁻⁷ = 0.999999815
The approximation after the first term comes from eliminating very small polynomial higher order terms.
The number of excited CO2 not quenched by collision is 0.244×10²²x0.999999815
That is almost a certainty that all CO2 molecules in a “bending” vibration state will radiate 15 microns.
The radiation density is the energy of a 15 micron photon times the number of radiating CO2 molecules. The energy of a 15 micron photon = 1.3 10⁻²⁰ J
The total radiation energy of all 15 micron photons in a cubic meter
= 0.244×10²² x 1.3 10⁻²⁰ Joules = 0.317 x 10² J
The average radiation energy per cubic meter per second is
31.7 J / 0.335 s = 95 Watts.
Conclusion:
The resulting radiation density at atmospheric pressure and 15℃ is around 95 Watts radiating isotropically within a cubic meter at 15℃ . Radiation is a far faster mode of energy transfer than conduction. The role of GHG radiation in the atmosphere energy transfer should not be underestimated.
The short answer:
A molecule vibrating in the15 micron radiation mode can hold that energy for 0.335 seconds.
The number of molecular collisions during that time is over a billion. However the vast majority of those collisions will simply bounce off without changing the molecular vibration state. Because of that, almost all CO2 molecules will keep their energy until they emit 15 micron radiation into the atmosphere.
The long answer:
These are the details of the short answer:
https://apps.dtic.mil/dtic/tr/fulltext/u2/771554.pdf from Table V
The average lifetime of a CO2 molecule in a bending vibration mode (15 micron radiation wavelength)
is 0.335 seconds.
Frequency of Molecular Collisions
The average atmospheric molecular collision frequency is 3.25×10⁹ collisions/second.
If just one of those billions of collisions were able to quench the CO2 vibrations, the probability of a CO2 radiating would be roughly 1 / 3.25×10⁹x0.335 which is 1 in 1.09 billion.
At first sight it would seem that the collision rate is so high that, for practical purposes all radiation vanishes. However inelastic collisions that would quench a CO2 vibration state are rare. Elastic collisions simply bounce off without changing any internal energy and are predominant.
https://pure.tue.nl/ws/files/3478579/109243.pdf “On Vibrational Relaxations in Carbon Dioxide”
TABLE III Translational Transition Probabilities Page 33.
This table gives the probabilities that a collision will quench a CO2 molecule in a 15 micron bending mode. The second column shows the probability is Pd² = 2.0 10⁻¹³ at 300 K. An extrapolation to the global average temperature of 288 K temperature gives a quenching collision probability = 1.7×10⁻¹³. That probability is very small.
Number of CO2 molecules per m³ @ 400ppm = 1.01×10²².
The number of atmospheric CO2 molecules in a 15 micron excitation state is
1.01×10²² x 2/9 = 0.244×10²² (2/9 comes from Equipartition Principle)
The probability that a single collision will quench that excited state = 1.7×10⁻¹³
The probability that a single collision does not quench the excited state = (1- 1.7×10⁻¹³)
The probability that none of the 1.09 billion collisions quenches the excited state =
(1 − 1.7×10⁻¹³)^1.09×10⁶ ≅ 1 − 1.7×10⁻¹³ × 1.09×10⁶ = 1 − 1.853×10⁻⁷ = 0.999999815
The approximation after the first term comes from eliminating very small polynomial higher order terms.
The number of excited CO2 not quenched by collision is 0.244×10²²x0.999999815
That is almost a certainty that all CO2 molecules in a “bending” vibration state will radiate 15 microns.
The radiation density is the energy of a 15 micron photon times the number of radiating CO2 molecules. The energy of a 15 micron photon = 1.3 10⁻²⁰ J
The total radiation energy of all 15 micron photons in a cubic meter
= 0.244×10²² x 1.3 10⁻²⁰ Joules = 0.317 x 10² J
The average radiation energy per cubic meter per second is
31.7 J / 0.335 s = 95 Watts.
Conclusion:
The resulting radiation density at atmospheric pressure and 15℃ is around 95 Watts radiating isotropically within a cubic meter at 15℃ . Radiation is a far faster mode of energy transfer than conduction. The role of GHG radiation in the atmosphere energy transfer should not be underestimated.
