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The temperature of a gas is usually the sum of the kinetic energy of its particles, right?

Whereas the temperature of a solid object is given by the Stefan-Bolzmann equation, as a function of how much thermal radiation it emits:

$$j^* = σT^4$$ (from Wikipedia, Stefan-Bolzmann equation)

But when you expose a greenhouse gas such as CO2 to infrared (IR) radiation, which is a form of thermal radiation, it too starts emitting IR radiation in all directions. If the IR exposure stops, the gas too very soon stops emitting IR, within a femtosecond or so, and the IR energy absorbed by the gas as excited vibrations is not normally converted into kinetic energy, as I've understood. (Even though it COULD possibly be converted into kinetic energy during a collision with another molecule, but this is unusual, right?) But still, for as long as the gas is exposed to IR radiation, it can exert both kinetic energy and IR energy on its surrounding.

So what is the temperature of the greenhouse gas? Is it still just the kinetic energy, as for other gases, or is it the kinetic energy plus the IR energy? Or does it have two separate types of temperature, one for kinetics and one for IR, and they can't be combined?

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    $\begingroup$ No, it's wrong. $\endgroup$
    – Debanjan Biswas
    Commented Dec 28, 2022 at 8:58
  • $\begingroup$ Are you assuming that only greenhouse gases emit thermal radiation and other gases don't? $\endgroup$
    – toxicPsychotic
    Commented Dec 28, 2022 at 11:26
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    $\begingroup$ Hi Karolina. Polyatomic molecules like CO₂ have rotational and vibrational energy, not just kinetic energy. When CO₂ absorbs IR light that energy is stored as vibrational energy. When you're working out the temperature of the gas you have to include the rotational and vibrational energy in your calculations. $\endgroup$
    – John Rennie
    Commented Dec 28, 2022 at 11:35
  • $\begingroup$ Gas does radiate all the time, not only when exposed to IR. At the same time it absorbs radiation from other sources, so the net effect may seem like no radiation in some cases. $\endgroup$
    – Tomáš Létal
    Commented Dec 28, 2022 at 12:23
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    $\begingroup$ @KarolinaHagegård the Stefan-Boltzmann law is not applicable to gases. The temperature of a gas is not simply related to how much IR it radiates. There is a relationship between temperature and radiation for a gas but it is different for every gas as it depends on the emission spectrum. Many gases like O₂ and N₂ barely radiate at all in the IR. In this respect the (few) greenhouse gases are unusual. $\endgroup$
    – John Rennie
    Commented Dec 28, 2022 at 17:20

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