Cooling down by radiation - a single molecule's point of view

[CaptainPanic]

Imagine an ideal gas that is cooling down by radiation (it's probably in space somewhere, and it's warmer than it's surroundings).

 

The individual gas molecules have to emit a photon in order to cool down (probably, but not necessarily, in the infrared).

 

What happens at the moment that a photon is emitted? It must mean that the molecule is colder now. Temperature and velocity of a gas molecule are related (velocity is a function of the square root of the velocity). So, does the molecule instantly slow down?

 

And can this photon be emitted just in mid-flight of the molecule (without interaction with a second molecule), or only when it collides or interacts with another gas molecule? Does the emission of the photon have any influence on the trajectory of the molecule?

 

Some Friday afternoon questions from a chemical engineer.

[Mr Skeptic]

Remember also that a photon has momentum as well as energy. I'm not sure how much it matters for this.

 

Anyhow, most emissions in the infrared are due to vibrations within a molecule. After emitting the photon, the vibrations are slower. Slower vibrations mean less kinetic energy. However, there is an equilibrium between the translational energy and the vibrational energy. Thus, when this slower vibrating molecule collides with others, its vibrational energy will probably increase, at the expense of translational kinetic energy.

[J.C.MacSwell]

Imagine an ideal gas that is cooling down by radiation (it's probably in space somewhere, and it's warmer than it's surroundings).

 

The individual gas molecules have to emit a photon in order to cool down (probably, but not necessarily, in the infrared).

 

What happens at the moment that a photon is emitted? It must mean that the molecule is colder now. Temperature and velocity of a gas molecule are related (velocity is a function of the square root of the velocity). So, does the molecule instantly slow down?

 

And can this photon be emitted just in mid-flight of the molecule (without interaction with a second molecule), or only when it collides or interacts with another gas molecule? Does the emission of the photon have any influence on the trajectory of the molecule?

 

Some Friday afternoon questions from a chemical engineer.

 

It should be during the acceleration phase *. There must be a correlation between the acceleration and the wavelength. There must also be a momentum balance (as well as energy balance) so the photon would have to influence the trajectory of the interacting molecules.

 

Edit: * I just read Skeptics post, which makes sense, so the molecule itself need not necessarily be accelerating, but there should be an acceleration involved.

Edited November 6, 2009 by J.C.MacSwell

[swansont]

You've described half of laser cooling emitting photons definitely changes the velocity of the emitting molecule. The emitted photon need not be in the IR, though, and you can't talk about the temperature of an individual atom or molecule.

[CaptainPanic]

You've described half of laser cooling emitting photons definitely changes the velocity of the emitting molecule. The emitted photon need not be in the IR, though, and you can't talk about the temperature of an individual atom or molecule.

 

You're right - I should have said that the mean velocity of the molecules (plural) in a gas is related to the square root of the temperature.

[Sorcerer]

Remember also that a photon has momentum as well as energy. I'm not sure how much it matters for this.

 

Anyhow, most emissions in the infrared are due to vibrations within a molecule. After emitting the photon, the vibrations are slower. Slower vibrations mean less kinetic energy. However, there is an equilibrium between the translational energy and the vibrational energy. Thus, when this slower vibrating molecule collides with others, its vibrational energy will probably increase, at the expense of translational kinetic energy.

 

I've always wondered about the word vibrate, is that just an analogy?

[swansont]

I've always wondered about the word vibrate, is that just an analogy?

 

No, it's an apt description of what happens when a collection of particles have kinetic energy but there is no overall center-of-mass motion. So atoms in a lattice actually vibrate, and in a molecule there is also vibration of the constituent molecules.