Temperature of a electron?

• eminent_youtom
In summary, scientists have detected electromagnetic waves, specifically in the x-ray spectrum, radiated by black holes, indicating that they have a temperature due to the vibration of atoms within the system. The interior structure of black holes remains largely speculative, but their temperature is a well-established concept in physics.

eminent_youtom

Hi there,
I was wondering from few weeks that what is a temperature? According to the classical idea, temperature is caused by the vibration (oscillation) of molecules and atoms. So, is it appropriate to ask the temperature of a single electron or few electrons? till what level temperature exists? what actually is temperature? what happens to the atoms, especially electrons, when we decrease the temperature of the system to the absolute zero, like if we cool it to near absolute zero temeprature?

Temperature is a statistical quantity. The formal definition is dS/dE, the change in entropy with respect to energy holding volume and particle number constant. Typically, a practical definition comes from the fact that the atoms, molecules, or whatever particles in your system have average kinetic energy &lt;KE&gt; = 3/2 kT, where k is Boltzmann's constant. (This does not apply in the case of a highly degenerate fermi gas, such as electrons in a solid.) Note too that the average specifically means to average over the KE of all the particles in your system, so it is not correct to take the KE of a random particle in the sample, multiply by 2/(3k) and call that its temperature.

In summary, it does not make sense to ask what the temperature of a single electron, atom, molecule, or even a handful of such particles. So you ask, at what scale does temperature 'kick in' where it makes sense to talk about temperature? Probably around a few million particles, although I don't think there is any set rule. I would say that if you had some large system, and you cut in in half, and whatever means you had for measuring the temperature gives you the same result for both halves without large fluctuations, then you're ok talking about temperature.

Classically speaking, if you lower the temperature to absolute zero, the atoms stop moving. This is not actually the case in quantum mechanics, because zero point motion would be left (you can think of it as an expression of the uncertainty principle; if you knew that p=0 from zero temperature, and the position was fixed, that would violate the UP, so things have to keep moving).

Electrons don't change their behavior much at low temperatures, thanks to the exclusion principle. Basically, they are required to fill available states from the lowest up, with only one to each state. The highest filled state defines the energy scale for electrons, in temperature units it's several(/ten-) thousand K. At any temperature that's a fair amount below this temperature, they act basically the same. So cooling to absolute zero from room temperature (300K) does virtually nothing to them.

Kanato, I believe you mean T = dE/dS (great answer otherwise).

Mapes said:
Kanato, I believe you mean T = dE/dS (great answer otherwise).

Heh whoops, yeah, that's what I meant :)

kanato said:
In summary, it does not make sense to ask what the temperature of a single electron, atom, molecule, or even a handful of such particles.

Does energy has a temperature? i am talking about the pure energy without any mass. otherwise if there are masses, certainly energy is going to to increase the temperature of the masses.
The main reason behind my question is the temperature of black holes. Stephen Hawking argued that pair of virtual particles are created near the event horizon [quantum fluctuation due to uncertainty principle], due to which black holes are radiating energy. Which means black holes have some temperature. It is widely accepted fact.

HOWEVER, black holes are such a system where spacetime fabric is wrapped in such a way that, tremendous masses are squeezed in a small volume. i.e. all the atoms and particle are squeezed together, where even atom doesn't exists in a pure atomic form. According to NASA, http://www.gsfc.nasa.gov/scienceques2002/20030516.htm" [Broken]
now my question is, how is it possible to have vibration of atoms in black holes? what is allowing them to vibrate (if they exists)? Although the mathematics behind the temperature of black holes are well estlablished, couldn't it be just a theoritical idea? because, particles are almost freezed inside the black hole.
so far, have scientists detected any electromagnetic wave radiated by black holes?

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I don't know what pure energy is, without mass, if it's not light. A system of photons does have temperature. Temperature is related to the energy and entropy of a system, so if the system has internal degrees of freedom (different ways to distribute the energy to the particles inside the system) then it has a temperature.

You question on black holes is better directed at another board, probably the
High Energy, Nuclear, Particle Physics board, or the Cosmology board. I think the interior structure of a black hole is probably something that remains highly speculative at this point, but I don't know.

eminent_youtom said:
so far, have scientists detected any electromagnetic wave radiated by black holes?
Yes. To my knowledge, the x-ray signature (caused by ionization of collapsing atoms) of black holes is one of the easiest ways to detect them.

1. What is the temperature of an electron?

The temperature of an electron is not well-defined, as it is a fundamental particle and does not have a physical size that can be measured. Therefore, it does not have a specific temperature like larger objects do.

2. Can the temperature of an electron be measured?

No, the temperature of an electron cannot be measured directly. However, it can be indirectly inferred by measuring the energy or velocity of the electrons in a system.

3. How does the temperature of an electron affect its behavior?

The temperature of an electron is related to its kinetic energy, which affects its behavior. Higher temperatures lead to higher kinetic energies, making the electrons more active and increasing the likelihood of them colliding with other particles.

4. What is the relationship between the temperature of an electron and the temperature of its surroundings?

The temperature of an electron is typically much lower than the temperature of its surroundings, due to its small size and lack of internal energy storage. However, it can still be influenced by the surrounding temperature and will tend to reach thermal equilibrium with its surroundings over time.

5. What is the typical temperature range of electrons in different environments?

The temperature of electrons can vary greatly depending on their environment. In a typical metal conductor, the electrons may have a temperature of around 10,000 Kelvin due to their high kinetic energy. In a plasma, the electrons can reach temperatures of millions of degrees Kelvin. In space, the electrons in the cosmic microwave background radiation have a temperature of 2.7 Kelvin.