Temperature and non-equilbrium thermodynamics

• pervect

pervect

Staff Emeritus
Suppose we have a body that isn't a black body, but has an arbitrary emission spectrum. In the general case, can the radiation from this body be characterized as having a temperature, and if so, how? If not, what conditions are needed to make the concept of temperature meaningful in this case?

This is an interesting question. All bodies that are in thermal equilibrium, radiate according to Planck's law, and when we define temperature, we define it either in canonical ensemble, or via zeroth law of thermodynamics, each of which is based on the principle that in order to measure temperature, there needs to be thermodynamical equilibrium between the apparatus and the object.

Those objects which are not in equilibrium, are changing their state towards an equilibrium state. However, temperature isn't a well defined concept in this transition period as far as I know, but it can be defined locally. For example if we have a system in which we wish to regulate temperature, and it's an open system so in general it is not in equilibrium, if we can locally measure temperature in the system, that is, interpolate the system as being locally in equilibrium while globally being in non-equilibrium state, then we can approximate the definition of temperature we got in normal thermodynamics.

Suppose we have a body that isn't a black body, but has an arbitrary emission spectrum. In the general case, can the radiation from this body be characterized as having a temperature, and if so, how? If not, what conditions are needed to make the concept of temperature meaningful in this case?
How about a monochromatic laser? In that case, we don't talk about temperature, we talk about frequency and energy.

vanhees71
How about a monochromatic laser? In that case, we don't talk about temperature, we talk about frequency and energy.
I don't see how we can ever relate temperature to the radiation itself until it interacts with matter... or am I missing something obvious here?

Yes I am aware of blackbody radiation. The radiation has a certain power output and energy density, but temperature is a measure of average particle kinetic energy in some phase of matter. Then again, I suppose you could measure the average energy of the photons in blackbody radiation and call it a temperature... the fact that it is blackbody radiation, thus traveling in all directions equally and at the same energy density, allows this to be done, similar to how a given quantity of matter must be in thermal equilibrium to have a meaningful temperature measured across its entirety? I've always thought of temperature as a property of matter caused by radiation in some way, but I can see how temperature can be related here. Is my understanding above correct?

Think of an electric stove. The stove top glows red, then white, then blue-white. The Sun looks yellow. Other stars look red or blue-white. Don't you see how those colors can be related to the temperature of the emitter? You seem to be saying it is only the temperature of the receiver that counts, or that the light has to be received at all for the emitter to have a temperature.

You seem to be saying it is only the temperature of the receiver that counts, or that the light has to be received at all for the emitter to have a temperature.
What I am saying is that it is either the emitter or the receiver that has a temperature, in the sense that the average kinetic energy of these particles (with mass) can be measured, compared to the radiation itself, in which only its average electromagnetic energy can be measured. My impression from what you are saying (and what I've googled) is that blackbody radiation (i.e. the radiation itself, not the emitter which obviously has a temperature) can have its own temperature, despite there being no way to measure the average kinetic energy of the photons.

anorlunda
My impression from what you are saying (and what I've googled) is that blackbody radiation (i.e. the radiation itself, not the emitter which obviously has a temperature) can have its own temperature, despite there being no way to measure the average kinetic energy of the photons.
That's right. For example particle genesis at the time of the big bang. According to that theory, before there were any massive particles of any kind, there was temperature.

By the way, the energy of a photon E=hf. We don't use the word kinetic for that. Low and high energy photons all move at speed c in a vacuum.

Kinetic energy of particles is one way to define temperature; it is not the only way.

https://en.wikipedia.org/wiki/Baryogenesis

Comeback City
Suppose we have a body that isn't a black body, but has an arbitrary emission spectrum. In the general case, can the radiation from this body be characterized as having a temperature, and if so, how? If not, what conditions are needed to make the concept of temperature meaningful in this case?

One way to think about blackbody radiation is that if you start by assuming the electromagnetic field (within a cavity) is at thermal equilibrium (meaning it has a well-defined temperature), then the spectrum of the field is given by Planck's spectral distribution. If the electromagentic spectrum is not a blackbody spectrum, you really can't assign it a temperature. A blackbody spectrum with a single frequency missing can be thought of as closely approximating a thermal radiation spectrum, but light from other sources (laser light, for the other extreme) simply cannot be thought of as an equilibrium distribution and so cannot be assigned a temperature.

According to that theory, before there were any massive particles of any kind, there was temperature.
This makes more sense now... I had always read (not quite understood though, haha) about there being temperature scales immediately following the big bang, but I never made the connection that massive particles hadn't theoretically formed yet. Thank you for the clarification

anorlunda