# Photons and temperature

## Main Question or Discussion Point

Can a photon be said to have a temperature? I want to know if temperature is still related to kinetic energy in this instance. If so, what determines its kinetic energy?

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russ_watters
Mentor
Photons don't have kinetic energy, just momentum. In particles, kinetic energy is proportional to temperature (and a function of mass).

For light, the frequency corresponds to the temperature that generated it.

(Q)
Russ

Doesn’t a photon increase its frequency by trading potential energy for kinetic energy when it falls into a gravitational field, and loses kinetic energy climbing out?

chroot
Staff Emeritus
Gold Member
You cannot assign a temperature to one single photon, just as you cannot assign a temperature to one single atom of matter. The statistics of temperature are just that -- statistics. At any given temperature, photons can have a wide range of energies -- as can individual atoms in a gas. By observing a large number of photons (or atoms), one can define a characteristic temperature for the ensemble. The spread of photon energies is described by the blackbody radiation law. For a normal thermal photon source, you can measure the spectrum and match it to the best blackbody spectrum. The temperature of the source is the same as the characteristic temperature of the best-fit blackbody spectrum.

So the photons do not individually have a temperature; but in large numbers you can describe the spectrum by a characteristic temperature.

- Warren

for example, the "background" microwave radiation that permeates the universe "has a temperature" of ~2.5K.
( see, for example: http://physics.about.com/library/weekly/aa021403a.htm )

Also, a photon field can be analysed in a Stat Mech way, with the same "thermal" properties (like entropy, pressure, chemical potential etc) as gasses and liquids.

Les Sleeth
Gold Member
Originally posted by chroot
So the photons do not individually have a temperature; but in large numbers you can describe the spectrum by a characteristic temperature.
I wonder if you agree with Russ Watters that photons have no kinetic energy? Isn't that what determines their frequency?

chroot
Staff Emeritus
Gold Member
Photons have energy, which is related to their momenta by E = pc. They do not have "kinetic energy" in the normal sense. Kinetic energy refers to energy stored in an object by making it move. You could define kinetic energy as follows: When you slow anobject down until it's stopped [in your frame of reference], the energy released used to be kinetic energy.

However, you can't slow down (or speed up) a photon, so really the concepts of "kinetic energy," "rest mass," and so on are misleading when applied to photons. The only way to slow them down is to destroy them.

Photons have no mass, and therefore no kinetic energy; all they have is momentum.

- Warren

Les Sleeth
Gold Member
Originally posted by chroot
Photons have no mass, and therefore no kinetic energy; all they have is momentum.

So, what sort of energy is it that is increasing/decreasing frequency?

chroot
Staff Emeritus
Gold Member
Total energy -- not specifically kinetic energy.

- Warren

(Q)
Chroot

Doesn’t this represent the kinetic energy of a photon?

pc=hc/wavelength

I alway think of it like : zero rest mass, times an infinite \gamma => non zero KE and p

Joe

chroot
Staff Emeritus
Gold Member
Originally posted by (Q)
Chroot

Doesn’t this represent the kinetic energy of a photon?

pc=hc/wavelength
We may be descending into semantics -- but I wouldn't call E = pc "kinetic energy." I'd just call it "energy."

- Warren

A "single" photon confined (with uncertainty of measurement) in a box with a certain volume gives an apparent distribution of many photons characteristic to the dimensions and thermal equilibrium of that box. From its energy volume density (aT4 in vacuum) of photons we assign a temperature.