What is considered low temperature in Debye/Einstein theories?

[gemt]

Hi,

This may seem basic bit but it is causing me a little confusion, any help would be appreseated.

In theories such as Debye / Einstein it is stated that it this is true for low temperatures, coudl someone tell me what sort of temerautres they acutally mean by this? do they mean low as in below 273K?? or a little higher.

Thanks

gem

 

[HallsofIvy]

Hi,

This may seem basic bit but it is causing me a little confusion, any help would be appreseated.

In theories such as Debye / Einstein it is stated that it this is true for low temperatures, coudl someone tell me what sort of temerautres they acutally mean by this? do they mean low as in below 273K?? or a little higher.

Thanks

gem

No, they couldn't mean that because -273 (more correctly about -273.15..) is absolute zero and it is impossible to have a temperature below that. They mean within one or two degrees of absolute zero.

 

[Swampeast Mike]

Hi,

This may seem basic bit but it is causing me a little confusion, any help would be appreseated.

In theories such as Debye / Einstein it is stated that it this is true for low temperatures, coudl someone tell me what sort of temerautres they acutally mean by this? do they mean low as in below 273K?? or a little higher.

Thanks

gem

Here is how I "see" temperature.

From our perspective as an observer on an atom's nucleus, temperature is a general representation of the distance to the electron "cloud". At perfectly regular interval we will find a given electron at one of two perfectly predictable elevations. Viewed three dimensionally however the distance between where it was found "low" and found "high" will change yet the electron has moved at a constant rate of speed. While we would think we're seeing a single, inpenetrable shell if we looked closely enough we would see two distinct shells alternating between low and high each of which instantly appears the instant the other disappears.

As the relative height of both shells increases, the disconnect in difference between which the electrons appeared to move and the speed at which they actually can move will grow such grown manifesting itself in what we feel as "temperature". The greater the volume inside the shells and the greater their distance between one another, the hotter the atom will seem.

 

[HallsofIvy]

Here is how I "see" temperature.

From our perspective as an observer on an atom's nucleus, temperature is a general representation of the distance to the electron "cloud". At perfectly regular interval we will find a given electron at one of two perfectly predictable elevations. Viewed three dimensionally however the distance between where it was found "low" and found "high" will change yet the electron has moved at a constant rate of speed. While we would think we're seeing a single, inpenetrable shell if we looked closely enough we would see two distinct shells alternating between low and high each of which instantly appears the instant the other disappears.

As the relative height of both shells increases, the disconnect in difference between which the electrons appeared to move and the speed at which they actually can move will grow such grown manifesting itself in what we feel as "temperature". The greater the volume inside the shells and the greater their distance between one another, the hotter the atom will seem.

That's nonsense. A single atom does not HAVE a temperature. Temperature relates to the average speed of the random motion of a group of molecules.

 

[Gokul43201]

Hi,

This may seem basic bit but it is causing me a little confusion, any help would be appreseated.

In theories such as Debye / Einstein it is stated that it this is true for low temperatures, coudl someone tell me what sort of temerautres they acutally mean by this? do they mean low as in below 273K?? or a little higher.

Thanks
gem

It depends on the model in question, but for many problems in solid state physics a few K is a low temperature.

In the Debye model, a low temperature is any temperature that is small compared to the Debye temperature (in 3D systems) or the Fermi Temperature (in lower dimensional systems). For most metals, the Debye Temperature is on the order of a few hundred K. So, the low temperature limit applies for say T<10K.

In the Einstein model, the characteristic temperature scale is the Einstein temperature, which, in that model is essentially the phonon energy. This number can be in the ballpark of a few tens of K to a few hundreds.

 

[Andy Resnick]

As others have stated, "low temperature" is taken as a statement of energy: to mean that thermal energy (considered a noise term) is insignificant compared to some aspect of interest. The specific temperature depends on what you are studying.

 

[f95toli]

That's nonsense. A single atom does not HAVE a temperature. Temperature relates to the average speed of the random motion of a group of molecules.

Even that is somewhat of a simplification. In solid state physics the word "temperature" has many different meanings, the most "general" definition is probably that the word refers to the shape of a distribution function of a specific subsystem, or in the case of systems with discrete levels to the population of different levels (so that zero temperature simply means that the system is always in its ground state).
But even this "definition" fails in cases where people talk about e.g. cooling of a single mode of a nanomechanical resonator.

 

[Renge Ishyo]

In theories such as Debye / Einstein it is stated that it this is true for low temperatures, coudl someone tell me what sort of temerautres they acutally mean by this? do they mean low as in below 273K?? or a little higher.

They mean temperatures "low enough" such that electrons cannot populate all of the possible energy levels for the given system. The temperature ranges in the Debye/Einstein theory where the heat capacity is not constant and not approximately equal to 3/2 are those in which the temperature is so low that some of the energy states that are available to the system at higher temps are not occupied at all for lower temps. Once the temperature raises to a certain point, for temperatures higher than that you can show that the heat capacity remains essentially constant at 3/2 from that point forward because there is at least some population existing in every available energy level. What is "low temperature" in this context varies from system to system (different materials have different energy level requirements..)...