What is temperature in non-molecule substance?

Main Question or Discussion Point

What is temperature in non-molecule substance(e.g photon,phonon,plasma...and radiations),because the definition of temperature is the average value of kinetic(motion) energy of the molecules of the substance.
Thank you very much in advance.

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Bill_K
This is not the definition. The absolute temperature of a system is defined in terms of its entropy. Calculate the entropy S(U, V) as a function of internal energy U and volume V. The first law of thermodynamics for a system at constant volume is dU = T dS, and consequently ∂S/∂U ≡ 1/T defines T. The internal energy can arise from kinetic energy, but includes other forms as well.

So,the entropy must be difined from the probability notion,but not from ''energy'' definition.Is that correct?

I think we must define entropy as the ''measure'' of chaos,but not through dQ/T to define the temperature in ''non-molecule'' substance.Is that correct?

Because We difine temperature through entropy!

Andrew Mason
Homework Helper
This is not the definition. The absolute temperature of a system is defined in terms of its entropy. Calculate the entropy S(U, V) as a function of internal energy U and volume V. The first law of thermodynamics for a system at constant volume is dU = T dS, and consequently ∂S/∂U ≡ 1/T defines T. The internal energy can arise from kinetic energy, but includes other forms as well.
Because We difine temperature through entropy!
So how does one define entropy without using temperature?

AM

Bill_K
The definition of entropy is a hot-button topic, guaranteed to draw 40-50 responses. Better to just refer you to the Wikipedia article http://en.wikipedia.org/wiki/Entropy.

"Just call it entropy. Nobody knows what entropy really is, so in a debate you will always have the advantage." -- John von Neumann

a microstate specifies all molecular details about the system including the position and velocity of every molecule
Well Bill, here is an extract from your reference to a statistical definition.

It clearly does not answer the OP since it refers to molecules.

I would say that the Wiki article is very 'light touch' in that is skips gaily over the difficult issues.

Let us explore the OP (which is a very good question) more fully because even totally non material 'objects' such as empty space have a temperature!

Andrew Mason
Homework Helper
The definition of entropy is a hot-button topic, guaranteed to draw 40-50 responses. Better to just refer you to the Wikipedia article http://en.wikipedia.org/wiki/Entropy.

"Just call it entropy. Nobody knows what entropy really is, so in a debate you will always have the advantage." -- John von Neumann
It was more of a rhetorical question because I don't think one can define thermodynamic entropy without reference to temperature. The units of entropy are energy/temperature (eg. Joules/Kelvin).

BTW I would not recommend the Wikipedia article on entropy. There are many incorrect and misleading statements.

As the OP points out, temperature is a well understood thermodynamic concept for matter: it is a measure of the translational kinetic energy of the molecules that comprise the matter. For matter in thermal equilibrium, the kinetic energy distribution follows a Maxwell-Boltzmann distribution curve from which the temperature can be determined (ie. it is the point on the curve such that a vertical line through that point divides the area under the curve into two equal parts).

I think the question is: what does temperature mean where the temperature is associated with something other than matter? eg. the photons in a blackbody cavity emitting blackbody radiation. In such a cavity matter is not the source of radiation. Yet we say that the blackbody has a temperature.

This is a very good question that is requires more than a simple answer. I'll start an answer and perhaps others can correct or add to it:

The temperature of a blackbody spectrum is determined by the energy distribution curve for the radiation, the same way that the temperature of a body of matter can be determined by the distribution curve. (The only difference is that photons bouncing around in a blackbody resonator obey Bose-Einstein statistics, not Maxwell-Boltzmann statistics. But the distribution curves are practically the same for high energies). We say that the temperature of the blackbody spectrum is a measure of the average energy of the photons comprising the radiation spectrum.

So whereas the temperature of matter in thermal equilibrium is a measure of the average translational kinetic energy of the molecules that comprise the matter, the temperature of radiation is determined by a point on the energy distribution curve of that radiation that corresponds to the average energy of the photons in the blackbody spectrum.

Note: Temperature is only defined for a blackbody spectrum of radiation. A laser which emits light of only one frequency, does not have a temperature.

AM

Andy Resnick
What is temperature in non-molecule substance(e.g photon,phonon,plasma...and radiations),because the definition of temperature is the average value of kinetic(motion) energy of the molecules of the substance.
Thank you very much in advance.
I am unaware of any reasonable definition that does not explicitly require some notion of equilibrium- for example, it's possible to assign a temperature to blackbody radiation. But, blackbody radiation is a radiation field in equilibrium with a thermal reservoir. I have not seen a detailed derivation, but it's surely possible to define a phonon field in thermal equilibrium with a reservoir, and then derive the spectral properties of such a 'blackbody speaker'.

By contrast, laser light does not have a well-defined temperature. For any nonequilibrium system, defining the entropy and temperature is not yet a settled question.

I have heard that there are many type of entropy e.g Shanon,von Newmann entropy...Some of them use in black hole,in ''informatics'' science...Moreover there is a formula called Bolzman formula that relates the normal entropy with the probability of thermal system(S=klnW).Then I think that we could use a suitable entropy to define the temperature.But I do not understand we need the equiblirium condition or not.

It seems that the entropy be consider even in both equilibrium and non-equilibrium process.But temperature notion exists in considering equilibrium process.Is that correct?

It seems that the entropy be consider even in both equilibrium and non-equilibrium process.But temperature notion exists in considering equilibrium process.Is that correct?
Perhaps you should consider what you mean by equilibrium.

A system is only in a state of equilibrium when there is no change to the variable under consideration in that system.

Two systems are defined to be at the same temperature when there is zero heat flow between them if they are placed in contact.

I think it is worth bearing in mind that following the theory of dimensions we can conclude all of mechanical theory with three (fundameental) quantities -usually taken as mass, length and time.
To include thermal theory we have to introduce a fourth quantity, usually temperature.
To include electrodynamic theory we have to include a fifth quantity, usually charge.

A differernt set applies at the quantum level.

It is not known if there are other quantities yet to be discovered.